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Improving operational service delivery through: 1. Simulation of alternative waiting line (queue) designs 2. Facility layout redesign 3. Organisational management and labour relations
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Improving Operational Service Delivery
at Stellenbosch Traffic Department
Luguen E. Gass
Department of Industrial Engineering
University of Stellenbosch
Study Leader: James Bekker
Final year project presented in partial fulfilment of the requirements for the
degree of Industrial Engineering at Stellenbosch University
B. Eng Industrial
December 2012
ToStellenbosch Traffic Department
and the National Department of Transport...May this be another step forward in
government service delivery.
i
Declaration
I, Luguen E. Gass, hereby declare that the work contained in this final
year project is my own original work and that I have not previously, in its
entirety or in part, submitted it at any university for a degree.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
LE. Gass Date
ii
ECSA Exit Level Outcomes Reference
Outcome Reference
Sections Pages
1. Problem solving: Demonstrate competence toidentify, assess, formulate and solve convergentand divergent engineering problems creatively andinnovatively.
All All
5. Engineering methods, skills and tools, includ-ing information technology: Demonstrate com-petence to use appropriate engineering methods,skills and tools, including those based on informa-tion technology.
2, 3, 4, 5 & 6 9 – 63
6. Professional and technical communication:Demonstrate competence to communicate effec-tively, both orally and in writing, with engineeringaudiences and the community at large.
All All
9. Independent learning ability: Demonstratecompetence to engage in independent learningthrough well developed learning skills.
2, 3 & 4 9 – 46
10. Engineering professionalism: Demonstratecritical awareness of the need to act professionallyand ethically and to exercise judgment and takeresponsibility within own limits of competence.
7 64 – 66
iii
Acknowledgements
My greatest thanks goes to God; without Him I could not.
I would also like to acknowledge Mr. (soon to be Dr.) James Bekker for
sharing his wealth of knowledge, answering all my questions timeously, and
for wearing his heart on his sleeve. It was comforting to have had his support
all the way.
Mr. Royi of the Stellenbosch Traffic department; thank you for providing a
playground in which to perform this final year project. A special thanks to
all the staff at the department who had to endure my nosiness for extended
periods of time.
My dearest friends who provided some trivial knowledge which usually re-
sulted in some good ideas; the days together make life worth so much more.
A special mention to Ulla who provided me with enough distraction to take
this project lightly, to Nina who makes “cray-cray” normal, and Caelli, who
so dutifully stands by me no matter what (and who converted my messy
cartoon ideas into a reality). I love you.
A last thanks to my parents responsible for producing this brain and brawn;
capable of producing and affecting this world - hopefully in a positive way.
To those not mentioned - know that you have impacted my life even if in
even the smallest way, and for that I am grateful.
iv
Abstract
The Stellenbosch Traffic Department offers a municipal service to approxi-
mately 40 000 vehicle owners in the area. Numerous complaints about ser-
vice delivery, specifically referring to the long times waited by customers at
the department, have been reported. The focus of this report is on the queu-
ing dilemma at the department and aims to investigate alternative models
to reduce extensive waiting times. A decision support system (DSS) in the
form of a stochastic, discrete-event simulation model is developed. Using
the DSS, four alternative models are experimented with. Results analysed
by TOPSIS show that the current queue model implemented at the de-
partment is sub-optimal and that a multiple-server-single-queue model is
likely to be a better solution; reducing the time in system for customers by
almost four times. Structural changes to the Stellenbosch facility are also
recommended to accommodate the multiple-server-single-queue model. Fi-
nally, managerial recommendations are provided such that employee morale
and leadership may be increased to further improve customer service at the
department.
v
Opsomming
Die Stellenbosch Verkeersdepartement lewer ’n munisipale diens aan ongeveer
40 000 voertuig eienaars in die area. Talle klagtes oor dienslewering, spesi-
fiek met betrekking tot die lang tye gewag deur kliente by die departement,
is aangemeld. Die fokus van hierdie verslag is op die toustaan-dilemma by
die departement en het ten doel om ondersoek in te stel na alternatiewe
modelle om uitgebreide wagtye te verminder. ’n Besluitnemingsonderste-
uningstelsel in die vorm van ’n stogastiese, diskrete simulasiemodel is on-
twikkel. Die Besluitnemingsondersteuningstelsel is gebruik om met vier
alternatiewe modelle te eksperimenteer. Resultate ontleed deur TOPSIS
toon dat die huidige toustaan model wat by die departement geimple-
menteer is, sub-optimaal is, en dat ’n meervoudige-bediener-enkeltou model
waarskynlik ’n beter oplossing is; wagtye is ongeveer vier keer vermindered.
Dit beveel ook strukturele veranderings aan die Stellenbosch-fasiliteit aan
om die meervoudige-bediener-enkeltou model te akkommodeer. Ten slotte,
bestuursaanbevelings is gegee sodat werknemermoraal en leierskap kan toe-
neem om verdere kliente diens by die departement te verbeter.
vi
Contents
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Business Process Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Solving Methodologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.1 Queuing Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Project Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Report Road Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Literature Review 9
2.1 Queuing Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Fundamental Concepts . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.2 Customer Behaviour . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Characterising the Problem . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 Input Analysis and Parameters . . . . . . . . . . . . . . . . . . . 15
2.2.3 Validation and Verification . . . . . . . . . . . . . . . . . . . . . 18
2.3 Queuing Theory vs. Simulation . . . . . . . . . . . . . . . . . . . . . . . 19
2.4 TOPSIS Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5 Box Plot Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.6 Managerial Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.6.1 Customer Waiting Time . . . . . . . . . . . . . . . . . . . . . . . 23
2.6.2 Organisational Behaviour . . . . . . . . . . . . . . . . . . . . . . 25
2.6.2.1 Work Motivation . . . . . . . . . . . . . . . . . . . . . . 25
2.6.2.2 Stress Management . . . . . . . . . . . . . . . . . . . . 27
vii
CONTENTS
2.6.2.3 Leadership . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.7 Summary of Literature Review . . . . . . . . . . . . . . . . . . . . . . . 28
3 Benchmarking 29
3.1 Stellenbosch Traffic Department . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Bellville Traffic Department . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Durbanville Traffic Department . . . . . . . . . . . . . . . . . . . . . . . 34
3.4 Malmesbury Traffic Department . . . . . . . . . . . . . . . . . . . . . . 36
3.5 Summary of Benchmarks . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4 Proposed Queue Models 41
4.1 Queue Design Considerations . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 Alternative Queue Designs . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3 Summary of Proposed Changes . . . . . . . . . . . . . . . . . . . . . . . 44
5 Simulation Study 46
5.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.2 Analysis of Simulation Results . . . . . . . . . . . . . . . . . . . . . . . 48
5.3 Validation and Verification . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.4 Summary of Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . 53
6 Conclusions and Recommendations 54
6.1 Queueing Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6.2 Facility Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.3 Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.3.1 Work Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.3.2 Stress Management . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.3.3 Leadership . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.4 Further Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . 61
7 Closing Summary 63
7.1 Project summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.3 Contribution to Society . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.4 Lessons Learnt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
viii
CONTENTS
7.5 Denouement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
References 69
A Supporting Information 70
A.1 Newspaper Articles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
A.2 Project Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
A.3 Time Study Template . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
B Queuing Models 76
B.1 Alternative Queuing Models . . . . . . . . . . . . . . . . . . . . . . . . . 76
B.1.1 Multiple Servers, Multiple Queues . . . . . . . . . . . . . . . . . 76
B.1.2 Multiple Servers, Single Queue . . . . . . . . . . . . . . . . . . . 78
C Simulation Model Notes 82
C.1 Functional Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
C.1.1 Operational Sections . . . . . . . . . . . . . . . . . . . . . . . . . 82
C.1.2 Servers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
C.1.3 Customers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
C.1.4 Transactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
C.1.5 Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
C.1.6 Schedules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
C.2 Input and Output Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
C.2.1 Input Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
C.2.2 Output Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
C.3 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
C.4 Model Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
C.4.1 Design 1 — Single Stage, Multiple Queue, Single and Multiple
Server . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
C.4.2 Design 2 — Single Stage, Multiple Queue, Single Server . . . . . 87
C.4.3 Design 3 — Multiple Stage, Single Queue, Single Server . . . . . 87
C.4.4 Design 4 — Single Stage, Single Queue, Multiple Server . . . . . 88
C.5 Data Distributions Summary . . . . . . . . . . . . . . . . . . . . . . . . 88
C.6 TOPSIS Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
ix
CONTENTS
D Administration of the
Final Year Project 92
D.1 Meetings with the Study Leader . . . . . . . . . . . . . . . . . . . . . . 92
D.2 Summary Time Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
x
List of Figures
1.1 Graphic Summary of the Problem Statement, Methodology and Result. 8
2.1 Triangular Distribution as Estimated by Servers . . . . . . . . . . . . . 17
2.2 Herzberg’s Two Factor Theory of Motivation . . . . . . . . . . . . . . . 26
3.1 Current Business Process Flow and Facility Layout . . . . . . . . . . . . 31
3.2 Bellville Traffic Department: Licence & Registration, Reed Str . . . . . 33
3.3 Bellville Traffic Department: Drivers Licences, Bailey Rd . . . . . . . . 34
3.4 Durbanville Traffic Department: Licence & Registration, Oxford Str . . 35
3.5 Durbanville Traffic Department: Drivers Licences, Church Str . . . . . . 36
3.6 Malmesbury Traffic Department: All Transactions . . . . . . . . . . . . 37
4.1 Design 1 — Single Stage, Multiple Queue, Single and Multiple Server . 43
4.2 Design 2 — Single Stage, Multiple Queue, Single Server . . . . . . . . . 44
4.3 Design 3 — Multiple Stage, Single Queue, Single Server . . . . . . . . . 45
4.4 Design 4 — Single Stage, Single Queue, Multiple Server . . . . . . . . . 45
5.1 Box Plots Comparing TIS of Designs 1 and 4 (left), Designs 2 and 4
(right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6.1 Recommended Business Process Flow and Facility Layout . . . . . . . . 57
A.1 “Rotten service detrimental to the economy.” . . . . . . . . . . . . . . . 70
A.2 “Service doesn’t exist.” . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
A.3 “Officers react to complaints.” . . . . . . . . . . . . . . . . . . . . . . . 72
A.4 Planned Tasks and Deadlines for the Project. . . . . . . . . . . . . . . . 74
A.5 Time Study Template for Servers . . . . . . . . . . . . . . . . . . . . . . 75
xi
LIST OF FIGURES
D.1 Extract of Meeting Minutes: Meeting 6. . . . . . . . . . . . . . . . . . . 93
D.2 Summary Time Sheet as on 21 October 2012. . . . . . . . . . . . . . . . 94
xii
List of Tables
4.1 Summary of Alternative Queuing Models . . . . . . . . . . . . . . . . . 42
5.1 Summary of Simulation Results . . . . . . . . . . . . . . . . . . . . . . . 47
5.2 Ranked TOPSIS Analysis of 75th Percentile Results . . . . . . . . . . . 49
5.3 Actual vs. Simulated TIS: Design 1 . . . . . . . . . . . . . . . . . . . . . 52
5.4 Actual vs. Simulated Entities Created: Design 1 . . . . . . . . . . . . . 52
6.1 Comparison of Simulation Results of Current- and Proposed Queue Designs 55
B.1 P (j ≥ S) for the M/M/s Queueing System . . . . . . . . . . . . . . . . 79
C.1 Summary of (Fitted) Time Study Data Distributions . . . . . . . . . . . 89
C.2 TOPSIS Analysis of 75th Percentile Results . . . . . . . . . . . . . . . . 91
C.3 TOPSIS Analysis of 75th Percentile Results (continued) . . . . . . . . . 91
xiii
Nomenclature
Acronyms
CIS Customers in System
eNatis Electronic National Traffic Information System
HRK Hassler Register Kassen: Retail Information System
OPUS Information system used for capturing fines
TCS Total Control System
TIS Time in System
Greek Symbols
λ Average arrival rate
µ Average service rate
πi Steady-state probability where there are i entities in the
system
ρ Workload rate or traffic intensity
Roman Symbols
Ab Best alternative
Aw Worst Alternative
dib Distance between target alternative i and the best con-
dition Ab
xiv
Nomenclature
diw Distance between target alternative i and the worst con-
dition Aw
L Average number of entities in system (in queue and in
service)
Lq Average number of entities in queue
P (j ≥ S) Probability there are more entities in the system, j, than
servers, S, given a certain ρ
p-value Probability of obtaining a test statistic at least as ex-
treme as the observed statistic
rij Normalised matrix
Sib Similarity to best condition
S Number of servers in system
Tij Weighted normalised matrix
vj Performance measure ,j
W Average time in system (in queue and in service)
Terminology
Drivers Licence Section Operational department processing all transactions re-
lated to drivers’ licenses, including learners’ licences
Entity Material existence referring to customers in the simula-
tion
Fines Section Operational department processing all transactions re-
lated to fines
Floor Customer queuing and waiting area
Toxin Handler Person willing to listen to an individual’s issues
Idle Not in service
xv
Nomenclature
Indifference Zone Area of difference between the quartiles of box plots.
In queue Waiting in line but not yet in service
In Service Currently being served by a server
Licence & Registration Section Operational department processing all transactions re-
lated to licenses, registrations and roadworthies
Mode Number that appears most often in a set
Multiple Server More than one server
Queueing Discipline Nature in which entities move from the queue to service
Section Independent operational department
Server A resource for which entities compete. A teller.
Social Justice Justice exercised within a community based on princi-
ples of equality
Teller A resource for which entities compete, usually in queu-
ing. A server.
Utilisation (of server) is the time-average number of individual servers,
divided by the total number of servers
Variates A random variable with a numerical value that is defined
on a given sample space
xvi
Chapter 1
Introduction
This final year project aims to apply techniques, skills and vantages of Industrial Engi-
neering to recommend improvements to Stellenbosch Traffic Department in creating a
business process which flows naturally and serves clients efficiently. The proposed im-
provements should increase customer satisfaction by reducing time waited in queues and
improving customer service. Existing structures and information systems will be con-
sidered in proposing a re-engineered queuing system, facility layout, and management
style. It is expected that this project will make use of operations research methods,
simulation and facility design.
This chapter describes the background of the problem at the Stellenbosch Traffic
Department and the need to improve its processes, the possible use of queuing theory
and simulation as problem solving methodologies, as well as this project’s objectives and
road map. The Stellenbosch Traffic Department may be referred to as “the department”
throughout this report.
1.1 Background
The Stellenbosch Traffic Department serves a local population in excess of 200 000 cit-
izens (Stats SA, 2007). It provides a municipal service to the Stellenbosch community
in the form of testing and issuing roadworthy validations, renewal of licences, registra-
tions, issuing and renewal of new drivers’ licences, facilitation of learners’ licence tests
and processing payment of fines. The department experiences large volumes of human
traffic on a daily basis, in part due to the fact that it is situated in a university town
1
1.1 Background
catering for over 20 000 university and college students; they are at the most popular
age to acquire drivers’ licences (University of Stellenbosch, 2012). In doing so, it is
required to cater for indigenous residents of Stellenbosch as well as those originating
from neighbouring municipalities, but residing temporarily in Stellenbosch.
The author realised an opportunity to improve service delivery and reduce customer
waiting time at the department after experiencing the frustration of the department’s
current system. Recent articles published by the Eikestad News newspaper on 26
April, seen in Figures A.1 and A.2 in Appendix A, illustrate the reality of the issue at
hand and emphasize the frustration of the general public who perceive that the waiting
lines at the department are unnecessarily long. The reaction from the department is
also included in Figure A.3. The articles are in Afrikaans and are not translated on
the assumption that the reader is literate in Afrikaans, but also to ensure that the
expressions of the articles are left untainted.
An interview with the Administrative Traffic Chief at the department, Mr. A. Royi,
highlights a few issues regarding the processes at the department which contribute to
ill service delivery (Royi, 2012):
Enquiries The department has a general enquiries desk to which persons entering the
building report. Customers are advised as to what documentation is necessary
and are directed to join a queue at the required section: Fines, Licence & Reg-
istration or Drivers Licences. Enquiries has only one server who is able to assist
one client at a time. This means that a single server at Enquiries is required to
serve a queue containing as many clients as there are in three other queues which
are served by multiple tellers. This causes the queue at Enquiries to “explode”,
increasing the time customers spend at the department.
Fine Processing System The system which processes and receives payment of fines
operates independently from the national system used for all other transactions.
Fines are processed by a system called OPUS or TCS, whereas all other trans-
actions are processed using eNatis. The problem is that fines can only be paid
using the OPUS/TCS system.
It is here that an opportunity to integrate the OPUS/TCS and eNatis systems is realised
by the author.
2
1.2 Business Process Analysis
Drivers Licence Section There is a lack of capacity at the Drivers Licence section.
Currently, learners’ licence tests are only performed on Wednesdays, while drivers’
licences are issued and renewed on the remaining days due to a lack of physical
space.
The author realises the opportunity to re-engineer the layout of the facility.
Employee Absenteeism The department is experiencing a high occurrence of in-
termittent and “unnecessary” absenteeism. It is suspected that employees are
exhausted and that the department is under staffed.
The author is interested to determine whether the department is in fact understaffed
or whether its current staff are simply under utilised.
Payment Facilities Payment facilities are limited to cash, cheque or debit card only.
There is no provision made for credit cards as it is associated with high cash
handling fees. “The installed debit card facilities are also unreliable and therefore
signs are placed at the tellers to notify customers that no card facilities [are]
available.” Mr. Royi informed that all prices are set and governed by the National
Department of Transport and that they cannot implement any other fees locally
without it being approved nationally.
The limitation of payment methods serves as a frustration to clients, and could place
strain on the queuing system as numerous clients are required to draw money at an
ATM and re-enter the queue.
It was also highlighted that the department understands that service delivery is a
key priority, but that it has limited funds to make necessary improvements, and strict
laws and controls which prohibit implementation of any new systems that have not
been approved by the National Department of Transport.
What follows is an “as-is” analysis of the business events carried out at the Stellen-
bosch Traffic Department.
1.2 Business Process Analysis
The way in which the department currently executes transactions and the facility layout
which supports this, will be analyzed in this section.
3
1.3 Solving Methodologies
The department executes its services with a modular approach; each section (Fines,
Licence & Registrattion, Drivers Licences) is independent from the other, with separate
tellers and queues for each. For example, a customer who wants to pay a fine, but also
renew a license, is required to queue for each transaction separately by first queuing at
the Fines section and paying the fine, and then having to queue again at the Drivers
Licence section in order to complete the renewal process. The Fines-, Drivers Licence-,
and Licence & Registration sections are mutually exclusive and therefore cannot process
any other transaction types other than their own.
The structural facility layout supports the current modular style of executing busi-
ness events; each section has its own queue and waiting area, albeit insufficient and
confusing for customers. It is speculated by the author that customers are confused
because there is a lack of logical systems and flow within the building.
The next section will take a look at the assumed methodologies required to solve
the issues faced by the department as discussed in sections 1.1 and 1.2.
1.3 Solving Methodologies
This section will consider possible techniques applicable to the problem at the depart-
ment, as well as the reasoning behind their use. It is speculated that the root cause of
the lengthy waiting lines described in section 1.1 is the modular layout of the various
sections at the department, more so than the issues highlighted by Mr. Royi. This
section will explore two main Industrial Engineering techniques – queuing theory and
simulation – as problem solving methodologies.
1.3.1 Queuing Theory
Queuing theory is practical in measuring a system’s performance by calculating the
time a client can expect to wait in the line and the total time spent in the system;
that is time spent queuing and being served (Gross et al., 2008). These values aid in
designing a near optimal system. It is in this project’s interest to balance idle time
of servers against minimized customer waiting time, and the resources associated with
these. The design of the structural facility which will house the servers, the waiting
line and waiting room are also to be considered.
4
1.4 Project Objectives
The analysis of the waiting line at the department is one of many complexities; one
being the distribution of arrivals which varies non-uniformly with time. In attempting
to design an improved queuing facility and layout it will be necessary to iterate queuing
analysis to compare results for each proposed solution in order to identify near optimal
solutions (Kelton et al., 2010). Analysis by queuing theory forces the analyst to make
simplifying assumptions. Kelton et al. (2010) suggests that in making such assumptions,
the complexities of the system are avoided, thus questioning the validity of results. It
is here that the use of simulation is suggested in order to build a more valid model of
reality.
The next section considers the use of simulation for this project.
1.3.2 Simulation
Computer simulation is the imitation of the operation of a system and its internal
processes over time to draw conclusions about the system’s behaviour. Simulation
models are often used to predict the effect of changes to existing systems, as well as
predict the performance of new systems. Simulation gives an adequate analysis of
complex systems, more so than queuing theory. (Kelton et al., 2010) It is therefore
considered to be applied to this project in analysing the current system, and the effects
of proposed changes.
The next section describes the aim and scope of this project, followed by a project
road map.
1.4 Project Objectives
The main aim of this project is to re-design the transactional flow of the Stellenbosch
Traffic Department such that customers are served promptly and resources are used
near-optimally. This will require analysis of current processes and systems, and finding
better ways of executing them. It will consider the queuing system, layout of the
department and general management.
The author envisions a complete turn-around in service delivery and customer sat-
isfaction. It is also envisioned to propose that the outcomes of this project be imple-
mented at traffic departments nationally; an appeal made to the National Department
of Transport.
5
1.5 Report Road Map
The project plans to deal with the following aspects with the described level of
detail:
Waiting Line Analysis of the waiting line using queuing theory and simulation must
be done in detail. The only way to expect a valid and realistic result is by using
accurate data. Data distributions will be approximated, but within statistically
accepted error bands.
Facility Layout The project will include a redesign of the facility’s layout, especially
at the Drivers Licence section which is experiencing capacity constraints, as ex-
plained in section 1.1.
Resource Management Organisational behaviour and general management advice
will be provided to aid management at the department to implement proposed
solutions, and also to improve employee morale. The author suspects that the
high occurrence of sick-leave is as a direct result of poor company culture and
uncomfortable work environment. The most valuable resource of a business is its
human capital; an idea often ignored by management. This report will provide
an understanding of organisational behaviour to the reader and suggest straight
forward socially, psychologically and physically implementable improvements.
Results It is desired to provide results in quantitive tables, graphs and summaries.
The simulation model will include animation. These will be used to convince
external parties who are less technically inclined on the subject of its results and
consequences.
The project plan which outlines the specific activities, durations and due dates for this
project is supplied in Appendix A.2.
1.5 Report Road Map
This chapter stated the problems to be addressed by this final year project. It is realised
that simulation and queuing theory can be used to re-design the Stellenbosch Traffic
Department’s business processes in order to increase customer satisfaction.
Chapter 2 explores literature on queuing theory and simulation as problem solving
tools and briefly introduces managerial aspects. Chapter 3 details operations at the
6
1.5 Report Road Map
department as well as three local traffic departments in the Western Cape which are
used for benchmarking, while Chapter 4 develops proposed changes to be made at the
Stellenbosch Traffic Department, including strategic and operational changes. Chapter
5 presents an analysis of the simulation of the proposed changes suggested in Chapter 4.
Chapter 6 draws conclusions and makes recommendations to the department. Chapter
7 provides an overview of the final year project from the author’s perspective.
Figure 1.1 illustrates a summary of the problems experienced at the department,
and the road map followed in this report.
7
1.5 Report Road Map
Figure 1.1: Graphic Summary of the Problem Statement, Methodology and Result.
8
Chapter 2
Literature Review
The previous chapter introduced the problem to be solved at the Stellenbosch Traffic
Department and the aim of this report. It mentioned specific problem areas at the
department as identified by the Administrative Traffic Chief, Mr. Royi, and mentioned
that queuing theory and simulation can be used as tools in finding solutions for the
department. The project plan was also introduced.
This chapter includes a literature study of queuing theory and simulation. More
specifically, it elaborates on discrete-event modeling as solving means. Thereafter,
literature on managing queues and human capital is explored. Lastly, analysis by
TOPSIS and box plots is discussed.
2.1 Queuing Theory
This section covers the basics of queuing theory rather than queuing simulation. Fa-
miliarity with queuing and its terminology is imperative to building queuing models.
Most models of real operations are of queuing systems, whether it be queues of physical
objects or information. In this report, queueing will be considered for the flow of people
(the customers). Queuing theory is also used in the verification of simulation models,
to be discussed later in this report. (Kelton et al., 2010)
2.1.1 Fundamental Concepts
It is assumed that the reader is familiar with basic probability theory and the following
concepts: experiments, sample space, events, random variables, probability distribu-
9
2.1 Queuing Theory
tions, expected values, and steady-state.
A queue system is one in which entities arrive, wait in one or more queues, are
served, and then leave. If there are more than one servers serving a queue, the system
is called a multiple server queueing system. An entity is in service when it has left the
front of the queue and is being served by a server, and in queue if it is waiting in the
line but not yet in service. The system refers to the sum of the queue and in service
aspects. The queuing discipline stipulates the nature in which entities move from the
queue into service. These include last-in-first-out (LIFO), general discipline, and first-
in-first-out (FIFO), the latter being applicable to the Traffic Department problem since
customers who enter the waiting line are served in order of first arrival. (Kelton et al.,
2010)
This project aims to minimize customers’ time in system (TIS). This is the time
an entity (the customer) spends in the waiting line and in service. The time in system
of customers will be used as performance measure of the success of various queueing
designs suggested in this report because this is the main contributor to the lack of
customer satisfaction, in the author’s opinion. It is the only objective which aims to
be minimized in this project, describing this project as a single objective optimization
problem. However, it must be noted that having this as the only objective could result
in requiring infinitely many servers. To prevent this, the proposed re-designed facilities
will be analyzed while considering utilization of the servers. It would be economically
infeasible to employ an infinite number of servers, but have the servers under utilized
and waiting idle for most part of the day. (Kelton et al., 2010)
In general, queueing theory analysis is done for steady-state conditions, which in-
clude a few basic symbols. These symbols are defined in the Nomenclature of this
report for ease of reference. However, it is necessary to be acquainted with some queu-
ing terminology before it can be discussed:
Wq Average time in queue (excluding service time)
W Average time in system (in queue and in service)
Lq Average number of entities in queue
L Average number of entities in system (in queue and in service)
ρ Workload rate or traffic intensity
10
2.1 Queuing Theory
λ Average arrival rate
µ Average service rate
Relationships between these steady-state measures exist which make computing and
estimating other queueing characteristics fairly simple. The first and most important
of these relationships is Little’s Law which has been proven in detail by Ross (1970).
Little’s Law is
L = λW
Kelton et al. (2010) highlights the interesting fact that Little’s Law relates a time
average (W ) to an entity-based average (L). More specifically, Little’s Law can be
extended as
Lq = λWq
and intuitively,
W = Wq + E(S)
where E(S) is the expected service time. This simply says that the expected time of
an entity in the system is the sum of the expected time in the queue and the expected
time in service. These formulae enable one to algebraically calculate any of Wq, W , Lq
or L, if only λ and a single value of these is known.
2.1.2 Customer Behaviour
Customer behaviour plays a very important role in queuing systems. The above sections
assume that every customer entering a queue will remain in the system until served, and
that the customer remains in only one waiting line. However, a more realistic approach
considers bulk arrivals, balking, reneging and jockeying, as explained by Gross et al.
(2008):
Bulk Arrivals More than one customer enters the queue at an instant.
11
2.2 Simulation
Balking If customers wanting to enter the queue see k customers ahead of them,
they do not join the queue. Customers have different discouragement limits, k.
However, the customer’s discouragement is not only due to the number of people,
k, but also the speed with which the queue advances. A long, but fast-moving
queue might be deemed worth joining while a short, slow-moving queue might
not.
Reneging A customer joins a queue and then estimates whether the waiting time will
be intolerable. If it is, the person leaves the queue. Reneging can be described
by a pure mathematical function.
Jockeying A customer moves back- and forth between several queues to attain the
shortest waiting time. As realistic as this behaviour is, it is very difficult to pursue
analytically since the probability distributions describing the jockeying process
become complicated.
It is necessary to establish whether the behaviours described here are in fact realised
at the department. If so, it must then be decided which of these occurrences to include
during the simulation and analysis. It may, or may not be acceptable to ignore the
effect it will have on the accuracy of the methodology used.
2.2 Simulation
This section considers the power of simulation in queueing problems, methods of gath-
ering input data, and validation and verification.
Many computerised tools are available which are useful in making decisions to
solve real problems. One of these decision techniques is simulation. Central to most
simulation models is the queue. (Kelton et al., 2010)
Queues occur because facilities lack in capacity to handle the demand placed on
them. It is also difficult to accurately predict the demand placed on these facilities and
how much time is required to render service. Queueing analysis is usually characterised
by uncertainty of (Kelton et al., 2010):
• Level of demand
• Service time
12
2.2 Simulation
• Behaviour of entities (reneging customers, bulk arrivals, etc.)
The purpose of applying queueing analysis is to identify what is needed to create
an adequate service facility. If a service facility is too generous it will result in idle
employees. If the service facility is inadequate, excessive waiting time could result in
a loss of goodwill of the customers and could discourage customers from entering the
queue at all. (Kelton et al., 2010)
There are numerous algorithms which are useful in solving queueing problems. How-
ever, Proctor (1994) and Kelton et al. (2010) agree that simulation is a better suited
analytical means for complex systems because it provides a near optimal solution which
is more realistic than those acquired by pure mathematical models (queuing theory).
A system is deemed “complex” when it either cannot be expressed mathematically
without making unreasonable assumptions, or the formulation is too involved for eco-
nomical and practical purposes. Simulation does not make use of any algorithm, but
rather illustrates the performance of a system given a set of input parameters. (Kelton
et al., 2010) These parameters are discussed in greater detail later in this section.
Simulation is the preferred choice of business analysts because of its degree of realism
and the ease with which it can be understood by non-technical decision makers. It is the
ultimate solution for decision makers to experiment with various factors and scenarios
of a problem to determine a near optimal solution without physically interfering with
the system. (Hoover & Perry, 1989)
Simulation requires the taking of random samples from a probability distribution
which represents the real-world system being analysed. Before a simulation can be
performed, the distribution of events needs to be determined for the real-world problem.
(Proctor, 1994)
Various approaches to simulation and methods of acquiring the distribution of these
events are discussed in the following section.
2.2.1 Characterising the Problem
This section characterizes the simulation for this project in detail.
A model of a scenario in simulation is characterized into three classes (Kelton et al.,
2010):
• Static vs. Dynamic
13
2.2 Simulation
• Continuous vs. Discrete
• Deterministic vs. Stochastic
A static simulation is one in which time has no effect on the model’s structure and
operation. This implies that such a model can be simulated without considering the
effect of time. A dynamic model is where the issue of time is central to the changes
and flows in a system. (Kelton et al., 2010)
Dynamic models usually have state variables that describe the state of a simulated
system. For a queueing system, these variables would indicate the length of the queue,
the times of arrivals of customers, or whether a server is idle or in service. A system
is considered to be continuous if these variables change continuously over time. A
common example would be the flow of water in and out of a tank. If states of these
variables change only at specific instances of time, rather than continuously, then the
model is discrete. This is most applicable to queueing problems since state variables
only change value at the time of occurrence of discrete events such as a customer
entering the queue, or a server going from in service to idle. (Kelton et al., 2010)
A deterministic model is one in which all input values of the model are constant,
and non-random. A deterministic model will always return the same results, regardless
of the number of times the model is re-run. Such models are very rare and somewhat
unrealistic. Simulation models where input values vary randomly, or from some prob-
ability distribution, are stochastic. This is typical of most queueing problems in that
the service time at the counter varies for each client. However, these service times can
be characterised by a probability distribution. This means that a stochastic model is,
in essence, run by a random draw of a distribution of data. (Kelton et al., 2010)
That said, running such a model only once would show only what could happen.
As Kelton et al. (2010) explains, this would be like tossing a die only once, observing a
number 4, and concluding that the die is biased to always result in a 4. This shows that
the simulation model of a stochastic problem must be run multiple times to conclude
the system’s behaviour. However, simply re-running the simulation of the stochastic
model will actually give the exact same results. This is due to the fact that random
number generators created by software are in fact not random at all, and will produce
the exact same random numbers each time. The solution to this is to replicate the model
multiple times within the same execution. This will produce a different random output
14
2.2 Simulation
from each replication while the simulation software keeps track of the uncertainty in
the results. (Kelton et al., 2007)
It can be concluded that the queueing problem at the Stellenbosch Traffic Depart-
ment is one which is dynamic, discrete, and stochastic:
Dynamic Time plays a role in the model of the queuing system converting client
arrivals to clients having been served by the system.
Discrete Clients arrive and leave at specific time intervals. Decision variables are
allocated only integer values.
Stochastic The system is modeled as one with some random inputs (random arrivals
of clients requiring random service times).
This type of problem is most typically solved by simulation. In fact, simulation
software is specifically designed for such problems (Kelton et al., 2010).
2.2.2 Input Analysis and Parameters
This section aims to describe the data required for the simulation of the queuing prob-
lem at the department, method for determining data distributions, and random number
generation to run the simulation. It will also take a brief look at verification of simulated
results.
Kelton et al. (2010) says that the distribution of service times must be specified. It
is ideal to have such data available, or made available by a time study.
Since a time study requires that real world data be collected, it would seem most
logical to simply use this collected data as input for the simulation model, rather
than a more indirect approach of fitting a probability distribution to the data, and
then generating random variates from the fitted distribution. Kelton et al. (2010) and
(Bekker, 2012a) give a few reasons for using a fitted distribution:
• Simulations are required to run for very long times and many replications are
run to ensure statistically valid results. The simulation would simply run out
of real-world data unless a probability distribution is fitted from which infinitely
many random variates can be generated.
15
2.2 Simulation
• The collected data represents only the time period for which the data is physically
collected. That data does not necessarily show what could have been observed
at other times. Using only the collected data would limit the simulation, and
question its validity.
• Collected data is usually only observed for certain times and periods; the sample
size is small. This could result in “gaps” in the data where events could possibly
have occurred, but which simply were not observed during the physical data
collection.
It is realized that it is more convenient to fit a probability distribution to some collected
data, and then generate random variates from this. It also ensures validity of the
simulation results.
Two methods of fitting a distribution to collected data are considered for this
project:
Option 1: Estimated Service Time, Physical Time-Study of Arrivals
This method is as suggested by the study leader. It is suggested that the servers be
asked to estimate their shortest-, typical-, and longest service times. This data would
then be used to create a triangular distribution of service time, as in Figure 2.1, from
which the simulation can generate variates. This is an internationally accepted practice
(Bekker, 2012b). Physical collection of data for arrivals of customers could be done by
means of a time study.
Option 2: Physical Time-Study of Service Time and Arrivals
This method follows the typical procedure for determining data distributions as ex-
plained in Kelton et al. (2010). A physical time study of the service time of each server
is done, and the same for inter-arrivals of customers. This method will require more
time and effort than detailed in Option 1, and is less convenient.
Option 2 is chosen as it provides the most accurate input data. The following
paragraph outlines a few important guidelines for doing time studies correctly.
Freivalds & Niebel (2009) say that the analyst conducting the time study must be
able to inspire confidence, exercise judgement and develop a personal approach with
everyone with whom s/he comes into contact with in order to ensure its success. The an-
alyst should also be familiar with and understand the operations being studied. Among
16
2.2 Simulation
Probability, f(t)
Service Time Shortest Typical Longest
Figure 2.1: Triangular Distribution as Estimated by Servers
many useful guidelines, Freivalds & Niebel (2009) make a few suggestions applicable to
time studies at the department:
The Operator The person being studied should be made familiar with time study
procedures and practices, and should be convinced of the advantages of cooper-
ating – having confidence in time study methods, as well as the analyst.
At the Stellenbosch Traffic Department this was done by fostering a comfortable re-
lationship with the servers, while also informing them of the uses and benefits of the
proposed outcomes of this project. Employees were approached in a friendly manner,
giving opportunity to ask questions which were answered frankly and patiently. The
author realised that explaining time study techniques and its aims to the employees at
the department allowed for the most valid data to be captured.
Recording The analyst should record all information and allow for remarks and
sketches on the time study form. The analyst should be sensitive to writing
notes when the time-study subject is present; it creates a sense of suspicion.
The author considered this; only making notes once out of line of sight of the interviewee
or time study subject.
17
2.2 Simulation
Position of the Analyst The analyst should preferably stand out of line of sight
of the server. Also, the analyst should refrain from any conversation with the
employee during operation as this can cause distraction and affect the validity of
the data.
A time study form in which servers actually conduct their own time study was con-
sidered by the author. The form required servers to tick a box each time they serve a
customer. The template is shown in Appendix A.3. This would give an indication of
customers served per hour.
2.2.3 Validation and Verification
It is important to bear in mind that the simulation needs to be valid. If the simulation
is invalid, it is not a true representation of reality, and forfeits its use as a solution to
any problem being modeled (Kelton et al., 2010). In creating the simulation model,
the validity of the model must be considered at all times.
Kelton et al. (2010) emphasizes the importance of verifying that the simulated
model is a valid representation of reality. It is proven by this source that simulation
does provide near-optimal, true results. However, every model must be checked to
ensure that the specific simulation is correctly formulated and that the results are
true. Bekker (2012a) states that “verification allows us to confirm that we have built
the model right, whereas validation allows us to confirm that we have built the right
model.”
It is suggested that a set of expectations of the model’s results be set up before the
actual simulation. These expectations are commonly determined by common sense and
by use of analytical means such as queueing theory. Once the simulation is performed,
the expected results should be compared to the simulation’s results. If the results do
not correlate, a few reasons for the differences should be considered, and adjustments
made to the model.
A few reasons could include (Kelton et al., 2007):
• The model is incorrectly created in the simulation software (i.e. there is an error
in the model itself).
18
2.3 Queuing Theory vs. Simulation
• The assumption that the simulation should match the expected results is incor-
rect. Kelton et al. (2010) explains that a “warm-up period” can be used to remedy
this.
• A sampling error could exist. The simulation’s results correlate with the expec-
tation probabilistically, but the model has not been run for long enough, or the
results are being interpreted incorrectly.
If results correlate realistically, the simulation is deemed valid by verification (Kelton
et al., 2010).
2.3 Queuing Theory vs. Simulation
In comparing queueing theory to simulation it is noticed that queuing theory falls short
for complex systems. Calculation by queuing theory alone is exact and not subject to
statistical uncertainty. Simulation, on the other hand, is not exact and is associated
with statistical uncertainty. (Kelton et al., 2010) This will be discussed in greater detail
later in this report.
Queuing theory requires that assumptions be made, and in many real cases (es-
pecially complex systems) such assumptions can be incorrect and invalidate results.
Simulation is made to deal with short-term analysis of queueing, and allows for a more
realistic data distribution input. It requires fewer generalizations and assumptions such
that the most appropriate inter-arrival and service time distributions can be used to
almost identically mimic the real system. There is, however, a negative aspect of sim-
ulation; all results are statistical estimates and therefore must be analyzed by proper
statistical means in order to draw justified conclusions. (Kelton et al., 2010)
A brief overview of queuing theory and how it compares to simulation was given
in this section. The following section introduces TOPSIS as a means of analysing the
best alternative queueing model, once simulation results are acquired.
2.4 TOPSIS Analysis
The “Technique for Order of Preference by Similarity to Ideal Solution” (TOPSIS) is a
multi-criteria decision analysis method, related to Analytical Hierarchy Process (AHP)
decision making, which was developed by Hwang and Yoon in 1981 (Jahanshahloo
19
2.4 TOPSIS Analysis
et al., 2006). It is mentioned by Kim & Nelson (2001) that statistical procedures based
on ranking and selection theory, such as TOPSIS, are popular when the number of
alternative designs is small as they are easy to apply and interpret.
It is useful in choosing a best- or worst case of numerous alternatives. It is based
on the idea of choosing an alternative which has the shortest geometric distance from
the ideal solution, and the longest geometric distance from the least preferred solution.
It compares alternatives based on weightings of relative importance of a set of crite-
ria, normalising the scores for each criterion, and calculating the geometric distance.
(Jahanshahloo et al., 2006)
The following describes how TOPSIS analysis is performed (Jahanshahloo et al.,
2006):
Firstly, a matrix of m alternatives by n criteria is developed, where each combina-
tion is given as Xij , resulting in a matrix (Xij)mxn.
The matrix is then normalised to the form:
R = (rij)mxn,
where rij = Xij/Pmax(vj),
Pmax(vj) = max{vj},
for i = 1, 2, ...,m,
j = 1, 2, ...,n.
where vj refers to the performance measure, j.
Next, a weighting is assigned to each criterion, n, and the weighted normalised matrix
is calculated:
T = (tij)mxn,
= (wjrij)mxn,
for i = 1, 2, ...,m,
where wj = Wj/
n∑j=1
Wj,
n∑j=1
wj = 1.
Wj is the weight given to vj.
20
2.4 TOPSIS Analysis
Next, the best alternative (Aw) and worst alternative (Ab) is calculated using:
Aw = {〈max(tij |i = 1, 2, ...,m)|j ∈ J−〉, 〈min(tij |i = 1, 2, ...,m)|j ∈ J+〉}
≡ {twj |j = 1, 2, ..., n}
Ab = {〈min(tij |i = 1, 2, ...,m)|j ∈ J−〉, 〈max(tij |i = 1, 2, ...,m)|j ∈ J+〉}
≡ {tbj |j = 1, 2, ..., n}
where J+ = {j = 1, 2, ..., n|j associated with benefitting criteria,
J− = {j = 1, 2, ..., n|j associated with negative (cost) criteria.
The distance between the target alternative, i, and the worst condition, Aw, is
calculated using:
diw =
√√√√ n∑j=1
(tij − twj)2
and the same for the best condition, Ab:
dib =
√√√√ n∑j=1
(tij − tbj)2
for all i = 1, 2, ...,m.
The similarity to the best condition is calculated:
sib = diw/(dib + diw), 0 ≤ sib ≤ 1, i = 1, 2, ...,m.
Lastly, the alternatives are ranked according to sib (i = 1, 2, ...,m) where the alter-
native with the highest sib is the overall winner.
An important assumption of the TOPSIS method is that the criteria are mono-
tonically assigned; the weightings sum to 1, or 100%. The TOPSIS analysis consid-
ers trade-offs between criteria values of the outcomes which will be outputted by the
simulation. It provides a realistic method to analyse alternatives, compared to other
decision process models which might not consider the relative importance of criteria.
(Jahanshahloo et al., 2006)
TOPSIS will be used to determine the best alternative between the queue designs
simulated. The criteria will relate to the performance measures chosen to measure the
improvements of the model and will typically include:
21
2.5 Box Plot Analysis
• Time in system (TIS)
• Number of customers in system (CIS)
• Utilisation of servers
• Percentage of customers not served
The next section considers the use of box plots to analyse alternatives.
2.5 Box Plot Analysis
A box plot is a convenient way of graphically illustrating numerical data as a five
number summary; the sample minimum, lower quartile, median, upper quartile and
the maximum. It can be used to compare alternatives without making assumptions of
the statistical distribution of the data (Frigge et al., 1989).
In comparing box plots, when there is no overlap in the spread of data it can be
said that there is a definite difference between the alternatives compared. With boxes
overlapping, but not the medians, it is likely that there is a difference, but this is
not definite. Should boxes overlap with both medians, no difference can be claimed.
(Nayland College Mathematics, 2012) Somewhat contradictory, Kim & Nelson (2001)
say that choosing an alternative is not as definite as previously described. Instead, it
is suggested that there be an indifference zone set by the experimenter such that a
difference in boxes should be greater than the said indifference zone, else the difference
between the data should be considered practically insignificant (Kim & Nelson, 2001).
It is recommended by Bekker (2012b) that this zone be set to approximately 5%.
The next chapter introduces literature on customer waiting time and organisational
behaviour.
2.6 Managerial Aspects
The previous sections discussed literature on queueing theory, how it compares to sim-
ulation, simulation’s function as decision tool, data required for the simulation study,
TOPSIS analysis, and the use of box plots. This section provides evidence that cus-
tomer waiting time is a valid performance measure to be considered in order to improve
22
2.6 Managerial Aspects
the quality of service at the department. It also explores literature of organisational
behaviour.
2.6.1 Customer Waiting Time
This section explores the time a customer waits in the system as performance measure
and considers other factors contributing to perceived waiting time, in addition to actual
waiting time.
Customer waiting time is regarded as one of the most critical aspects of quality
in service. In the modern day, society is more time-constrained than ever before.
A competitive world in which the expectation to do more in less time is unlikely to
diminish. (Sheu et al., 2003) Extended waiting has been cited as an important source
of customer dissatisfaction in many service industries (Murdick et al., 1990). Customer
evaluation of service quality is partly determined by the time waited for a service,
therefore many companies have included waiting time as a measure of service quality
(Sheu & Babbar, 1996). This motivates why it is appropriate to use customer waiting
time as a performance measure for this project.
Service providers, such as the Stellenbosch Traffic Department, realise that cus-
tomers value time. A customer having to wait an “unreasonable” amount of time is
considered to be “wasting” time and this could prevent customers from entering the
queue at all. This is essentially saying that a customer waiting in a line is a lost cus-
tomer (Sheu et al., 2003). Any private organisation would lose this customer to its
competition.
However, this is slightly different for traffic departments in South Africa; vehicle
owners and drivers are obligated to perform certain transactions such as renewing their
licences or paying fines, by law, with no option to make use of a competing service
provider – all drivers residing in Stellenbosch are obligated to use the Stellenbosch
Traffic Department. This means that customers are forced to enter the waiting line at
some or other stage, regardless of the expected waiting time. The only motivation for
the department to reduce waiting time is to encourage all citizens to comply to South
Africa’s traffic laws. Improving the current system will encourage road users to pay
fines, roadworthy their vehicles, renew licences and acquire legal licenses – all of which
increase revenue for the municipality and make South African roads safer to use. It
will also reduce employee fatigue and improve morale. The advantages are “infinite”.
23
2.6 Managerial Aspects
Changes to a process can result in improvements with regards to actual waiting time
for a customer, but customer satisfaction might not be realised unless this improvement
is perceived by the customer. An article by Luo et al. (2003) suggests that perceived
waiting time is a more accurate predictor of customer satisfaction and is quite often
different from the actual waiting time, depending on how and what customers are
waiting for. An instance at Disney World is described (Luo et al., 2003):
“In Disney World, for instance, a number of popular rides make visitors wait for at
least 45 minutes to take a 3 minute ride, but most visitors are quite satisfied with their
experience. This is because the distractions employed by Disney make visitors feel that
they did not wait that long.”
This raises the question of what can be done, other than improving the actual
waiting time, to influence customers’ perceived waiting time at the traffic department.
It is suggested to change the service environment (Katz et al., 1991), engage with
customers during the wait (Dube & Schmidt, 1996), and to provide feedback of expected
waiting time (Hui & Zhou, 1996). Another example shows where feedback reduced the
dissatisfaction of waiting (Luo et al., 2003):
“Hui & Zhou (1996) conducted an experiment in which university students were
instructed to use an online course registration system with system delay. Under one
condition, students were informed about how long the delay was going to be, and under
another, there was no delay information. The results showed that delay information did
not change students’ perceived waiting time, but students felt they had more control
over the wait. Providing delay information also reduced students’ dissatisfaction with
the delay.”
Maister (1985) has found that both customer perception and expectation about
a service operation play a role in determining customer satisfaction. If the customer
perceives that the service has exceeded his/her expectations, the customer is satisfied.
This says that a customer’s level of satisfaction can be influenced by adjusting his/her
expectation or perception of the service. On the same topic, Baker & Baker (1996)
suggest that a customer’s perception of waiting time can be influenced by changing a
customer’s perception of time, or of the queue. It is proposed that spatial layout, queue-
ing progress, and social justice are variables which can alter a customer’s perception of
a queue.
24
2.6 Managerial Aspects
On the other hand, a customer’s perception of time can be influenced by using
music, lighting, colour, employee visibility, and social interaction. The use of music is
found to have positive effects on a customer’s emotions toward waiting in a queue, but
has no effect on the perceived waiting time. (Hui & Dube, 1997)
In summary, in redesigning a service process, not only the actual waiting time, but
the perceived waiting time should also be considered. In the author’s opinion, perceived
waiting time cannot be quantified in a simulation and can only be measured once the
redesigned process has been implemented.
This section has shown that actual waiting time should not be the only focus of
process improvement at the department, but that perceived waiting time and customer
satisfaction should also be considered. It is also important to bear in mind that process
improvement might bring about unintended results. A small scale “pilot project” of
the proposed process change could initially be implemented in order to establish any
unintended effects.
2.6.2 Organisational Behaviour
This section discusses behavioural aspects of people in a work environment. The work
environment is required to facilitate organisational diversity and motivation, stress
management, leadership and communication within each employee.
2.6.2.1 Work Motivation
The author perceives that the employees of the department do not show interest in their
work and are generally unmotivated. The following literature discusses work motivation
and ways to improve it.
Motivation refers to the forces from within an individual that causes the person to
wilfully and persistently direct efforts toward achieving a goal, where the goal is not
achievable merely by the person’s physical abilities (Hitt et al., 2011).
Two theories for motivation exist: content- and process theories. Content theories
of motivation focus on identifying specific factors that motivate people. It is a straight
forward and traditional approach which includes McClelland’s Needs Theory, Alderfer’s
ERG Theory, and Herzberg’s Two-Factor Theory. (Hitt et al., 2011)
McClelland states that each person has a need for achievement, affiliation and power
in order to be motivated. These three needs are independent, meaning that a person
25
2.6 Managerial Aspects
Motivators
Hygienes
Satisfaction
No dissatisfaction
No Satisfaction
Dissatisfaction
Figure 2.2: Herzberg’s Two Factor Theory of Motivation
(Management Study Guide, 2012)
can be in varying stages of each need. Alderfer’s ERG Theory is similar to Maslow’s
well-known “Hierarchy of Needs” in that it puts forward basic needs which build on
one another. The levels are, starting from the most basic need, existence, relatedness,
and growth. Only once the need of existence is satisfied, can a person progress to
satisfy his/her need of relatedness, and then growth. Herzberg’s Two-Factor Theory
emphasizes the rewards and outcomes of a situation as motivator for performance.
Rewards are related to job satisfaction or job dissatisfaction, independently. (Hitt
et al., 2011) In other words, the antonym of job satisfaction is not dissatisfaction, but
rather low satisfaction, as illustrated in Figure 2.2.
In contrast to content theories, process theories consider the process by which fac-
tors result in motivation, rather than the factors themselves. This includes Vroom’s
Expectancy Theory, Equity Theory and Goal Setting.
Expectancy Theory states that there are multiple, complex sources of motivation.
It suggests that people consider three factors in establishing their level of effort: the
probability that effort will lead to performance (expectancy), the ratio of rewards likely
to be received for a particular performance level (instrumentality), and the relative
importance or value of the outcome (valence). (Hiriyappa, 2011)
Equity Theory simply states that a person’s motivation depends on his/her opinion
of how fair a situation is, and how s/he is being treated. Each person calculates the
ratio of equity in the expected outcomes versus their inputs, compared to other people
in the organisation. It also says that individuals adjust their effort according to their
opinion of equity. (Hitt et al., 2011)
Goal Setting Theory suggests that goals enhance human performance because they
26
2.6 Managerial Aspects
channel focus, attention and effort (Miner, 2005). Hitt et al. (2011) states that the
positive effects of goal setting on work motivation is “one of the strongest findings
in research on organisational behaviour.” It recommends that goals setting include
consideration of the goal difficulty, specificity, commitment, participation of associates,
and feedback of performance.
2.6.2.2 Stress Management
Mr. Royi mentions in section 1.1 that the department’s high occurrence of absen-
teeism could be attributed to the fact that employees are exhausted and stressed. This
paragraph discusses solutions in managing stress.
Hitt et al. (2011) suggests reducing organisational stress by increasing individu-
als’ autonomy and control, ensuring individuals are fairly rewarded for their effort,
maintaining job demands and requirements at healthy levels, ensuring that employees
have adequate skills for the job, increasing employee involvement in decision making,
improving physical work conditions, providing job security, career development and
healthy work schedules, improving communication throughout all job levels, encour-
aging managers to be “toxin handlers” who can listen and lend advice to individuals,
and implementing wellness programmes. It is important to realise that these actions
require involvement from management.
Individual stress management is also an important consideration. It is again sug-
gested by Hitt et al. (2011) that individuals participate in regular exercise, practise a
lifestyle which consists of a proper and balanced diet, involve themselves in social net-
works for support, and make use of relaxation techniques. This should be encouraged
by management at the department.
2.6.2.3 Leadership
It is suspected by the author that the department is experiencing a lack of organisa-
tional leadership. An article in Hitt et al. (2011) by Maria Yee, CEO of a furniture
manufacturing company in the USA, expresses her belief that leadership development
throughout the organisation is one of the top five factors contributing to gaining a com-
petitive advantage in the market. Warren Bennis, a leadership expert, says that leaders
should be “doing the right things” and not so much “doing things right” (Bennis, 2003).
27
2.7 Summary of Literature Review
Hitt et al. (2011) put forward various types of leadership theories which demonstrate
different behaviours and styles. In summary of this information, it is concluded that
leaders have traits and actions in line with:
• creating and communicating a vision of what the organisation should be,
• communicating with and gaining the support of each part of the company,
• persisting with a decided direction, regardless of the conditions,
• creating a company culture which supports the business and obtains results,
• having a drive and motivation to deliver,
• personal characteristics of integrity, confidence, knowledge of the business, and
cognitive ability, and
• being open to new experiences and solutions.
2.7 Summary of Literature Review
This chapter reviewed literature on simulation and queueing theory extensively. It
convinced the author that simulation is necessary to solve the queuing problem at the
department. It also discussed TOPSIS and box plots for analysing simulation results.
It then briefly explored literature on managing queues and people. The next chapter
describes the findings of benchmarking performed by the author at various local traffic
departments.
28
Chapter 3
Benchmarking
The previous chapter justified the use of simulation and customer waiting time as a
performance measure. It also explained behavioural aspects which could contribute to
improving service delivery at the department.
This chapter describes the process flows, operational management, and facility lay-
out of the Stellenbosch department and three local traffic departments, namely: Bel-
lville, Durbanville and Malmesbury. Bellville and Durbanville form part of the City
of Cape Town Municipality, while the latter is governed by Swartland Municipality.
The concept of benchmarking is used to investigate whether other traffic departments
are experiencing similar problems to the Stellenbosch department. It is also used in
generating alternative queue models to be simulated.
3.1 Stellenbosch Traffic Department
The Stellenbosch Traffic Department provides services to 41 883 customers; the total
number of registered vehicles in the district as on 30 September 2012 (Royi, 2012). The
department’s current facility layout, shown in Figure 3.1, does not allow all transactions
to be performed every day. The current layout at the Drivers Licence section limits
learners’ tests to be facilitated only on Wednesdays, while drivers’ licences are processed
on the remaining days.
The process flow of the current layout indicates numerous crossing paths which
prevent easy flow of customers in the system. The waiting area at the Drivers Licence
section serves no definite purpose; it is simply a “general” waiting area. Drivers Licence
29
3.1 Stellenbosch Traffic Department
enquiries and payments are done at the rear of the building which is confusing for
customers; most customers walk into the building having to search for the teller or
enquiries desk.
In Figure 3.1, notice the separation of the Fines-, Licence & Registration, and
Drivers Licence sections. The arrows indicate the sequential flow of customers. Ap-
proximately 10% of Licence & Registration customers require authorisation, and must
then re-enter at the front of the queue.
A few key operations are detailed:
Operating Hours From 08:00 – 15:00 for vehicle registrations at the Licence & Reg-
istration section, 08:00 – 15:30 for all other transactions, while employee working
hours are 07:30 – 16:00. Vehicle registrations are assumed to be the longest trans-
action type; this is the reason given for closing such applications 30 minutes prior
to other transactions (Royi, 2012).
Payment Method Cash or Cheque is preferred. Debit card facilities are available,
but are not used because they are “unreliable”. Credit card payments are not
allowed.
Authorisation Some transactions require authorisation from a supervisor before it
may be performed by a server. Customers are directed to the authorisation office
by the teller once the customer has already waited in the queue. Authorisation is
usually a lengthy process requiring an average of 10 minutes to process. A queue
usually forms outside the authorisation office, as shown in Figure 3.1.
Meetings These are held during operational hours and exclude participation of servers
who have to remain in operation to serve customers.
Lunch Breaks Each teller is allowed a maximum of one 30 minute lunch break, and
a 15 minute tea break, at self-decided times.
30
3.1 Stellenbosch Traffic Department
Enq
uir
ies
Licence & Registration Servers
Au
tho
risa
tio
nO
ffic
eSt
ore
1
Off
ice
Off
ice
Off
ice
Off
ice
Fin
es
Serv
er
Off
ice
Off
ice
Vau
lt
Dri
vers
’ Li
cen
ces
Serv
er
Lear
ner
s’ T
est
Ro
om
(Wed
nes
day
s)
Eye
Test
Wai
tin
g A
rea
(Mo
n,T
ues
, Th
urs
,Fri
)
Eye
Test
R
oo
m 1
Eye
Test
R
oo
m 2
Dri
vers
Lic
ence
sG
ener
alW
aiti
ng
Are
a
Sto
re 2
Off
ice
Off
ice
Off
ice
Sto
re Dri
vers
Lic
ence
s W
aiti
ng
Are
a
ENTR
AN
CE
(Mai
n B
uild
ing)
ENTR
AN
CE
Application Forms Station
Application Forms Station
Fin
es
Serv
er
Telle
r 2
Telle
r3
Enq
uir
es
Dri
vers
Lice
nce
sSe
rver
Enq
uir
ies
Telle
r1
Telle
r3
Au
tho
risa
tio
n
Serv
er
Eye
Test
O
ffic
er 1
Eye
Test
O
ffic
er 2
Application Forms Station
Off
ices
, Par
ade
Ro
om
, Kit
chen
Enter
Exit
Queue
Enter
Eye
Test
ExitDriv
ers Licences
Fines
Licence
& Regist
ratio
n
Authorisation
Exit
Fin
esLi
cen
ce &
Reg
istr
atio
nD
rive
rs L
icen
ces
Figure 3.1: Current Business Process Flow and Facility Layout
31
3.2 Bellville Traffic Department
3.2 Bellville Traffic Department
Bellville Traffic Department is split into three sections, not unlike the current layout
of the Stellenbosch department. Fines- and Licence & Registration transactions are
handled at the main building in Reed Street, with fines and roadworthies processed at
a single teller and licences and registrations performed at four other tellers, while all
Drivers Licence related transactions are performed in a building two streets away, in
Baily Road.
Licence & Registration type transactions are split into two parts: the application
and payment, and then the issuance. The customer goes to a server to apply and pay
for a transaction, and then waits in another queue to be issued the document, as shown
in Figure 3.2. This separation of roles was most likely introduced to prevent corruption
at the department. This gave the author the idea of an alternative queuing model in
which transactions are split into three parts: application, payment and issuance.
The Drivers Licences section at Bailey Road did not reveal any hassles with respect
to service delivery. On the contrary, the tellers at this section admittedly are idle quite
often. This suggests to the author that the excessive waiting time at the Licence &
Registration section may be reduced by making use of the Drivers Licences section’s
idle tellers. This would require integrating the Licence & Registration and Drivers
Licences sections in a single facility. The Drivers Licences section at Bellville has a
simple layout, as in Figure 3.3. The figure excludes the area for eye tests because
optimization of eye test administration is beyond the scope of this report. It was,
however, mentioned by Bellville department’s staff that the newly implemented eye
test machinery has lengthened the drivers licence process, and that the public should
be urged to make use of a service offered by optometrists in South Africa; an “Eye
Test Screening Certificate” can be obtained free of charge and used instead of having
to wait in a long queue at the Traffic Department for an eye test.
Employees and supervisors at the Licence & Registration section at Reed Street
refused to converse with the author which made obtaining any information difficult.
However, Mrs. Bronwyn Pieterson at the Drivers Licences section in Baily Road was
extremely insightful and willingly provided the author with information.
A few other key operations are highlighted below, to compare to that of the Stel-
lenbosch department (Pieterson, 2012):
32
3.2 Bellville Traffic Department
Teller 5Collection
Teller 4Application & Payment
Teller 6Collection
Teller 2Application Payment
Fines
Fines & Roadworthy
Start(Licence & Registration)
Start(Fines, Roadworthy)
Figure 3.2: Bellville Traffic Department: Licence & Registration, Reed Str
Operating Hours From 08:00 – 15:30 for all transactions, but employee working
hours are 07:30 – 16:00.
Payment Method Cash or Cheque only. Payment cannot be made using debit- nor
credit cards.
Authorisation There is insufficient information regarding authorisation at Reed Street.
Only on the rare occasion is authorisation required at the Drivers Licence section
on Baily Road.
Meetings No information about meetings at the Reed Street section was given. The
Drivers Licence section at Baily Road hosts short meetings approximately every
second week, before the start of the business day.
Lunch Breaks Each server is entitled to a maximum of 30 minutes for a lunch break,
and another 15 minutes for tea. The servers decide among themselves when they
will take these breaks.
Tellers are given only 30 minutes to complete their financial cash-ups at the end
of the business day. The tellers at the Drivers Licence section said that it usually
does not take longer than 15 minutes, but should the cash-up not balance, it can take
33
3.3 Durbanville Traffic Department
Teller 1
Teller 2
Drivers Licences
Figure 3.3: Bellville Traffic Department: Drivers Licences, Bailey Rd
up to a maximum of 30 minutes. It was also advised that all cash-ups are captured
on the HRK management system at the end of the day by one of the tellers or the
supervisor. (Pieterson, 2012) HRK is a cash management system which was noticed to
be implemented only at City of Cape Town Municipality Traffic Departments.
Mrs. Tanya Reid of Bellville Traffic Department mentioned that she has been
receiving numerous complaints from customers who have had to wait in excess of 30
minutes in the queue at the Licence & Registration section in Reed Street (Reid, 2012).
The process layout of this section is shown in Figure 3.2. The long waiting time is
synonymous with complaints at the Stellenbosch department. This instantiates the
author’s suspicion that the current separation of operational sections (Fines-, Licence
& Registration, Drivers Licences) is detrimental to the service level of the Stellenbosch
Traffic Department, as it is at Bellville.
3.3 Durbanville Traffic Department
Durbanville Traffic department is also split into three sections, similarly to the Stel-
lenbosch department. Licensing and registrations are done at a satellite office within
the Durbanville Municipality Administrative Offices building in Oxford Street, while
drivers licences, roadworthies and fines are processed at the main building in Church
34
3.3 Durbanville Traffic Department
Teller 3 Teller 4Teller 2 Teller 5
Teller 1
Start
Figure 3.4: Durbanville Traffic Department: Licence & Registration, Oxford Str
Street. The satellite office has approximately three open tellers who process Licence &
Registration type transactions, as in Figure 3.4.
The Drivers Licence and Roadworthy section in Church Street is perceived to be a
smooth running operation. Two enquiry tellers also accept payment of fines, while two
other tellers process drivers licences and roadworthy transactions. Incorporating fines
into enquiries may be a feasible option for Stellenbosch. The layout of Durbanville’s
Drivers Licence and Roadworthy section is shown in Figure 3.5.
This department is also open on two Saturdays of every month. A few operational
notes were made during the visit at the traffic department, as below:
Operating Hours From 08:00 – 15:30 for all transactions, but employee working
hours are 07:50 – 16:00.
Payment Method Cash or Cheque only. Payment cannot be made using debit- nor
credit cards.
Authorisation Insufficient information regarding authorisation at Reed and Church
Street.
Meetings Approximately every two weeks, if required. All personnel are included.
Lunch Breaks Each teller is allowed a maximum of one 45 minute lunch break, and
a 15 minute tea break, self-decided.
35
3.4 Malmesbury Traffic Department
Teller 4Drivers Licences &
Roadworthy
Enquiries& Fines
Enquiries& Fines
Teller 3Drivers Licences &
Roadworthy
Teller 2Drivers Licences &
Roadworthy
Teller 1Drivers Licences &
Roadworthy
Enquiries & Fines
Drivers Licence & Roadworthy
ExitExit
Figure 3.5: Durbanville Traffic Department: Drivers Licences, Church Str
3.4 Malmesbury Traffic Department
This traffic department is governed by the Swartland Municipality, unlike the aformen-
tioned municipalities which are governed under the City of Cape Town Municipality. As
shown in Figure 3.6, Malmesbury Traffic Department integrates all transaction types;
while fines are payable at one specific teller, all other transactions – licence & regis-
tration, roadworthies, and drivers’ licences – are done at any of four tellers at the end
of a single queue. Customers are required to enter one queue only, while tellers are
able to perform any transaction. Mr. Nico Edas and Mrs. Anita Nieuwoudt of the
Malmesbury department assisted in providing insightful information about the facility
and its operations (Edas, 2012) (Nieuwoudt, 2012):
Operating Hours From 08:00 – 15:00, closing 30 minutes before the previously dis-
cussed departments, but employee working hours are 07:50 – 16:00. On Fridays,
the department closes at 14:00, to compensate for shortened lunch breaks (see
“Lunch Breaks” below).
Payment Method Cash or Cheque only. Payment cannot be made using debit- nor
credit cards.
36
3.4 Malmesbury Traffic Department
Teller 2 Teller 3Teller 1 Teller 4
Fines
Start
Enqueries
Proposed NewEnqueries
Desk
Fines (Outsourced)
All Transactions:Licence & Registration, Drivers Licences, and Roadworthy Tellers Enqueries
Figure 3.6: Malmesbury Traffic Department: All Transactions
Authorisation Performed by the municipal representative or supervisor. Customers
are not required to go to a separate authorisation office, instead it is done while
the customer waits at the teller.
Meetings Every second Friday, at the end of the business day, all personnel included.
Lunch Breaks Each teller is allowed a maximum of one 45 minute lunch break, and
instead of a 15 minute tea break, the servers are allowed to finish work one hour
earlier on Fridays. Usually two of the four tellers take lunch at a time, in these
time slots: 12:15 – 13:00 or 13:00 – 13:45.
This traffic department has a dedicated Enquiries server, as Stellenbosch does.
Learners’ licence tests are written Mondays through Thursdays, but appointments
can be made any day of the week. Drivers licences can also be renewed every day.
This is unlike Stellenbosch which only allows learners’ licence tests to be performed on
Wednesdays, and drivers’ licences to be renewed on the remaining days.
37
3.4 Malmesbury Traffic Department
A few innovative and interesting ideas are being applied at Malmesbury Traffic
Department:
• The supervisor uses a Bluetoothr earpiece to answer all incoming calls and trans-
fers this to the Enquiries desk when unavailable to take calls. This allows the
supervisor to be flexible; remaining visible and assisting customers in the queue,
while being able to answer incoming calls.
• All application forms are issued to customers at the Enquiries desk. This guides
the customer to have all documentation ready for hassle-free service at the teller
and prevents frustration for the customer; usually customers enter the queue and
wait in the line only to be informed that they have insufficient documentation.
• This department has applied for a dynamic queue regulator which sends visual-
and voice commands to the customers in the queue to state which server is avail-
able.
• The supervisor tries to be active on the “floor” where most customer interaction
occurs. The supervisor is able to answer technical questions which Enquiries
might not have the answers to, is able to identify clients who require authorisation
even before they reach the teller, or allow customers who merely want to renew
their licences to bypass the queue because such transaction requires less than
60 seconds to process. This also puts customers at ease; literature in section
2.6.1 explains that having employees active and visible results in customers more
willing to bear the wait in the queue.
• In the case of authorisation, when the supervisor is not “on the floor”, the teller
simply phones the supervisor through the switchboard, and relays information
for the supervisor to process the authorisation without requiring the customer to
physically go to an authorisation office.
• This department also makes use of highly effective signage which guides customers
through the building. This ensures that customers are not confused about where
to go or what to do.
• All processed application forms are scanned and stored as soft copies on a database
for future reference.
38
3.5 Summary of Benchmarks
• There is a good work ethic and culture at Malmesbury Traffic Department; staff
are friendly and appear to enjoy their work environment.
3.5 Summary of Benchmarks
The previous sections detailed the key operations of various traffic departments sur-
rounding and including the Stellenbosch department. It provides a good perspective
of the challenges faced and operations at departments under the municipalities of the
City of Cape Town and Swartland.
Operating hours are relatively uniform. The Stellenbosch department is unique
in that it closes applications for vehicle registrations 30 minutes prior to the actual
closing time. The author perceives this as being unnecessary considering that three
other traffic departments do not take this approach, yet still manage to cash-up on
time.
Payment methods exclude the option to pay by debit- or credit card across the
benchmarks. This is due to the fact that the National Department of Transport excludes
cash handling fees in calculating transaction fees for Western Cape traffic departments.
The departments operate on strict budgets and therefore prefer curbing losses incurred
by card facility cash handling fees. Stellenbosch Traffic Department does have card
facilities, but does not accept credit cards. The department is also reluctant to use the
card facilities because they are unreliable (Royi, 2012).
Malmesbury Traffic Department displays truly innovative ways of delivering excep-
tional service and optimising resource utilisation. Their method of processing transac-
tions which require authorisation is unique in that it is customer-oriented, minimizing
the need for the customer to enter and re-enter the queue or proceed to a separate
office.
Meetings that include servers can only be held outside operational work hours. The
scenarios described in this chapter reveal that very few departments hold meetings
that include servers, if any. The author identified consensus amoung staff from all the
departments discussed in this chapter, that they would prefer to be included in weekly
or daily meetings, even if outside operational hours.
Lunch breaks vary slightly between the departments discussed in this chapter. It
can be said that servers are entitled to 45 minutes which includes a separate 15 minute
39
3.5 Summary of Benchmarks
tea break. Each department handles this differently. Malmesbury’s policy to close one
hour earlier on Fridays in exchange for servers sacrificing their tea breaks, provides one
hour additional serving time of the queue which contributes to the exceptional service
and short waiting times at the Malmesbury department.
Benchmarking has proven to be valuable to the author in generating ideas of alter-
native queueing designs which are revealed in the next chapter. It has also shown the
author what is possible and provides hope for what the Stellenbosch department may
achieve in the near future.
40
Chapter 4
Proposed Queue Models
This chapter considers various queuing models to be considered for Stellenbosch Traffic
Department. The first section introduces process design elements which should be
considered, and the second proposes queueing layouts as experiments to be analyzed
by simulation.
4.1 Queue Design Considerations
Service process design refers to the way in which facilities are laid out and the process
through which a service is delivered (Ramaswamy, 1996). Fitzsimmons & Fitzsim-
mons (2000) have suggested that when demand is highly fluctuating and peak demand
regularly exceeds capacity, cross-training of personnel should be considered.
The concept of cross-training requires every server to perform all transaction types,
as at Malmesbury. When this was mentioned, Mr. Royi indicated that there is concern
of such cross-training in terms of opportunity for corruption because employees will
have authority in a broad range of transactions. In the author’s, opinion a well designed
information system can control and monitor employees in such a way that corruption
and fraud are almost entirely curbed.
A further suggestion by Fitzsimmons & Fitzsimmons (2000) is to incorporate flexi-
bility into the design of the service process so as to respond to demand variations. This
will assist with optimising personnel utilization while reducing customer waiting time.
The following section introduces queue designs to be simulated.
41
4.2 Alternative Queue Designs
Table 4.1: Summary of Alternative Queuing Models
Idle Server (%) Time in System (minutes)
Example 1 25 12
Example 2 56.72 3.8
4.2 Alternative Queue Designs
Various queue designs are introduced in this section to be investigated through simu-
lation in order to determine the most effective design in terms of minimised customer
waiting time.
The author developed these designs using ideas generated as a direct result of bench-
marking, as well as a simplified mathematical comparison of multiple-server-multiple-
queue and multiple-server-single-queue model examples using queueing theory. The
queuing theory analysis is presented in detail in Appendix B, and is summarised in
Table 4.1.
Comparing the idle time (and therefore the utilization) and waiting time in each
example, the advantage of multiple servers serving a single queue rather than multiple
queues, can be seen. In Example 1, where multiple servers serve multiple queues,
servers are found to be idle 25% of the time, and customers spend an average of over
twelve minutes in the system. In Example 2, where multiple serves serve a single queue,
servers are idle over 50% of the time while customers are in the system for under four
minutes. Not only are the servers better utilised, but the customers also spend almost
four times less waiting in the system in the second example. Sheu & Babbar (1996)
suggests that a single-queue-multiple-server design (Example 2) always outperforms a
multiple-queue-multiple-server system (Example 1) in terms of customer waiting time.
Mr. Royi mentioned that the department is understaffed. By changing the layout
of the department to be one in which servers serve a single queue, the demand will be
reduced, thus reducing the need to employ more staff. Not only this – customers could
also expect to spend less time in a queue.
For this reason, this project considers a multiple-server-single-queue model as a
possible solution to the long waiting times at the department.
The author developed four designs to be simulated:
42
4.2 Alternative Queue Designs
Fines
Licensing & Registration
Licensing & Registration
Drivers Licences
Figure 4.1: Design 1 — Single Stage, Multiple Queue, Single and Multiple Server
Design 1 – Single Stage, Multiple Queue, Single and Multiple Servers This is
the current layout of the Stellenbosch Traffic Department. Example 1, analysed
in section B.1.1, represents the essence of Design 1; separate waiting lines are
formed at each section. Each server is limited to only one transaction type, as
seen in Figure 4.1.
The illustrations represent customers as circles and servers as squares.
Design 2 – Single Stage, Multiple Queue, Single Server Customers all enter into
any of four separate queues and can perform any type of transaction at a single
server. See Figure 4.2.
Design 3 – Multiple Stage, Single Queue, Single Server Stages of the transac-
tion are separated into the processing of the application, receiving of monies, and
issuing of documents, with a dedicated server at each stage. See Figure 4.3. This
is similar to the approach of a drive through restaurant; one person takes the
order, another receives payment, and the last person delivers the food.
43
4.3 Summary of Proposed Changes
All Transactions(Fines, Licensing &
Registration, Roadworthy,
Licences)
All Transactions(Fines, Licensing &
Registration, Roadworthy,
Licences)
All Transactions(Fines, Licensing &
Registration, Roadworthy,
Licences)
All Transactions(Fines, Licensing &
Registration, Roadworthy,
Licences)
Figure 4.2: Design 2 — Single Stage, Multiple Queue, Single Server
Design 4 – Single Stage, Single Queue, Multiple Server Customers all enter a
single queue and can be served by one of multiple servers – which ever server is
available next. See Figure 4.4. The essence of this design is captured in Example
2 of section B.1.2.
Design 3 could be a solution to Mr. Royi’s concern for corruption within the depart-
ment. Separating roles into three sections (application processing, payment, issuing)
would mean that any fraudulent transaction would have to be approved by three em-
ployees. The likeliness that three employees concede to fraudulent activity is probably
somewhat less than that of one person having sufficient authority to commit a fraudu-
lent transaction.
4.3 Summary of Proposed Changes
This chapter introduced the reader to queue models which form part of the solution
set in reducing customer waiting time. These models are developed and simulated in
the following chapter.
44
4.3 Summary of Proposed Changes
Issuance of Documents
Payment
Application
Figure 4.3: Design 3 — Multiple Stage, Single Queue, Single Server
All Transactions(Fines, Licensing &
Registration, Roadworthy,
Licences)
All Transactions(Fines, Licensing &
Registration, Roadworthy,
Licences)
All Transactions(Fines, Licensing &
Registration, Roadworthy,
Licences)
All Transactions(Fines, Licensing &
Registration, Roadworthy,
Licences)
Figure 4.4: Design 4 — Single Stage, Single Queue, Multiple Server
45
Chapter 5
Simulation Study
The previous chapters provided knowledge acquired leading up to the decision to sim-
ulate the current queue design at the department, as well as three alternatives. The
functional specification, detailed explanation of each model simulated and a summary
of input data used are provided in Appendix C. In this chapter, the simulation results
and the validation and verification of the models are presented and discussed.
5.1 Simulation Results
The previous section briefly introduced the models to be simulated. This section pro-
vides the reader with quantitive results as outputted by the simulations of each model.
The study leader recommended that the author use 75th percentile results from the
simulation for analysis. This was recommended to ensure statistically sound argument
(Bekker, 2012b). The simulation results are summarised in Table 5.1.
46
5.1 Simulation Results
Tab
le5.
1:S
um
mar
yof
Sim
ula
tion
Res
ult
s
Scenario
Perform
anceM
easu
re
Average
75th
Percentile
Min
imum
Maxim
um
Half
Wid
th
Design
1A
llS
erver
sU
tilisa
tion
,A
vg
(%)
66.0
375
68.5
458
56.5
275
77.2
406
0.2
321
Cu
stom
ers
inS
yst
em(C
IS),
Avg
18.3
760
21.5
247
6.2
401
36.2
884
0.3
023
Cu
stom
ers
Not
Ser
ved
(%)
13.3
574
15.5
488
3.3
537
22.8
916
0.2
002
Tim
ein
Syst
em(T
IS),
Avg
(min
ute
s)21.1
348
24.9
133
8.7
314
41.8
979
0.3
706
Oth
erPerform
anceM
easu
res
Cu
stom
ers
inS
yst
em(C
IS),
Max
52.0
000
59.0
000
20.0
000
89.0
000
0.6
668
Dri
ver
sL
icen
ceS
erver
Uti
lisa
tion
,A
vg
(%)
97.0
499
99.3
101
83.0
653
100.0
000
0.1
873
Fin
esS
erver
Uti
lisa
tion
,A
vg
(%)
15.3
582
17.5
589
6.6
633
25.9
288
0.2
086
Lic
ence
&R
egis
trati
on
Ser
ver
Uti
lisa
tion
,A
vg
(%)
75.8
710
80.7
000
54.7
406
99.9
982
0.4
439
Dri
ver
sL
icen
seC
IS,
Avg
8.4
205
11.2
778
1.5
894
24.5
390
0.2
666
Fin
esC
IS,
Avg
0.1
931
0.2
228
0.0
733
0.4
559
0.0
033
Lic
ense
&R
egis
trati
on
CIS
,A
vg
9.7
624
11.3
437
3.0
622
22.6
736
0.1
519
Lic
ence
&R
egis
trati
on
TIS
,A
vg
(min
ute
s)22.0
499
25.2
106
8.9
592
48.8
562
0.3
151
Design
2A
llS
erver
sU
tilisa
tion
,A
vg
(%)
60.7
245
62.9
562
50.3
348
72.4
108
0.1
909
Cu
stom
ers
inS
yst
em,
Avg
3.1
763
3.3
588
2.2
779
4.4
745
0.0
186
Cu
stom
ers
Not
Ser
ved
(%)
0.9
679
1.2
739
0.0
000
3.4
056
0.0
347
Tim
ein
Syst
em(T
IS),
Avg
(min
ute
s)4.4
010
4.5
860
3.5
378
5.8
870
0.0
193
Design
3A
llS
erver
sU
tilisa
tion
,A
vg
(%)
59.3
575
59.9
899
56.5
854
62.0
126
0.0
555
Cu
stom
ers
inS
yst
em,
Avg
49.0
895
55.0
176
19.6
259
82.3
618
0.5
763
Cu
stom
ers
Not
Ser
ved
(%)
28.7
502
31.4
465
16.3
763
39.4
595
0.2
336
Tim
ein
Syst
em(T
IS),
Avg
(min
ute
s)68.3
966
75.9
809
28.5
249
105.1
046
0.6
835
Design
4A
llS
erver
sU
tilisa
tion
,A
vg
(%)
60.7
649
63.0
218
52.0
465
70.2
152
0.1
971
Cu
stom
ers
inS
yst
em,
Avg
3.0
846
3.2
747
2.3
823
4.4
503
0.0
190
Cu
stom
ers
Not
Ser
ved
(%)
0.9
686
1.2
903
0.0
000
2.9
499
0.0
342
Tim
ein
Syst
em(T
IS),
Avg
(min
ute
s)4.2
706
4.4
396
3.5
655
6.2
614
0.0
203
47
5.2 Analysis of Simulation Results
5.2 Analysis of Simulation Results
The simulated results of Design 1 show that the Fines server is under utilised at only
17.56%, while the Drivers Licence server is operating at near maximum capacity with
a utilisation of 99.31%. The servers at the License & Registration section are only
utilised at 80.70%. From this, it is speculated that the waiting time can be reduced
and customer satisfaction improved by mobilising the Fines server to other sections. It
is with this intention that Design 2 and 4 make use of all servers for all transactions.
It is also seen here that the department operates with an average of 21.52 customers
in the system, and a maximum of 89, while 15.55% of all customers who enter the system
are not served. The fact that 15.55% of customers are not served is unacceptable. This
simulation once again proves the dire need for a re-design of the business processing
system at Stellenbosch Traffic Department and echoes the intention of this project.
Table 5.1 shows the significant improvement of Design 2 in contrast to Design 1;
customers are expected to spend an average of 4.4 minutes in the system, compared to
21.13 minutes of the current model implemented. There is also an expected reduction
in the average percentage of unserved customers in the system from 18.38% to 3.18%.
The simulation results for Design 3 are worse than that of the status quo in every
respect. See Table 5.1 for specific results.
At first glance, the results of Design 4 are marginally better than those of Design
2. This implies that the queuing models which allow servers to process all types of
transactions are superior to the other models simulated.
In order to identify and justify the best design, it is necessary to analyse the results
for each model simulated. As explained in section 2.4, TOPSIS is a multi-criteria
decision analysis method used in choosing a best- or worst case of numerous alternatives.
It compares alternatives based on weightings of relative importance of a set of criteria,
normalising the scores for each criterion, and calculating the geometric distance of
each. The TOPSIS calculations are shown in Appendix C.6, and the results ranked
and summarised in Table 5.2.
As mentioned previously, TOPSIS makes use of a weighting criterion. The author
has chosen the average time in system (TIS) to carry a weighting of 75%, with average
number of customers in system, server utilisation and percentage of customers not
48
5.2 Analysis of Simulation Results
Table 5.2: Ranked TOPSIS Analysis of 75th Percentile Results
TOPSIS Outcome
Model dib diw Sib Rank Sib Model
Design 1 0.20771 0.50838 0.7099 1 0.9949 Design 4
Design 2 0.00389 0.71359 0.9946 2 0.9946 Design 2
Design 3 0.71499 0.01040 0.0143 3 0.7099 Design 1
Design 4 0.00369 0.71502 0.9949 4 0.0143 Design 3
served carrying the remaining weight in equal proportions. Time in system (TIS) is
chosen as the majority criteria as this is the main concern at the department.
The TOPSIS analysis summary of Table 5.2 shows Design 4 as the superior queue
model because it has the greatest similarity to the best condition, Sib. Design 2 and
Design 4 differ marginally; a difference in scores of only 0.0003. From this it suspected
that Designs 2 and 4 are equally successful as a difference of 0.0003 is negligible in
statistical terms.
As a secondary method of evaluating the alternatives, box plots of the time in
system (TIS) are used to graphically identify whether there is a significant difference
between Designs 1 and 4. It is also used to further analyse whether there is a significant
difference between Designs 2 and 4, which differ insignificantly by TOPSIS analysis.
Refer to Figure 5.1.
The box plots show no overlap of data in comparing Design 1 and 4; this reaffirms
that Design 4 is superior by obtaining the lowest time in system (TIS). It is also clear
that the difference between the boxes are well over the 5% indifference zone, as discussed
in section 2.5. The comparison of Designs 2 and 4 show overlapping of medians; this
means that no difference between the time in system of these designs can be claimed.
However, it must be considered that the simulation of Design 2 assumes that cus-
tomers entering the system make perfect logical calculations in entering the shortest
of four queues. It is unlikely that every customer entering the system will make an
accurate calculation, the result being that the time in system (TIS) of Design 2 is likely
to be greater than outputted by the simulation. It is with this reason that the author
chooses Design 4 as the best queue design.
This section has shown from two perspectives that Designs 2 and 4 outperform
Design 1 in terms of time in system (TIS).
49
5.2 Analysis of Simulation Results
0
5
10
15
20
25
30
35
40
45
Design 1 Design 40
1
2
3
4
5
6
7
Design 2 Design 4
Figure 5.1: Box Plots Comparing TIS of Designs 1 and 4 (left), Designs 2 and 4 (right).
50
5.3 Validation and Verification
5.3 Validation and Verification
Kelton et al. (2010) recommends that simulation models should be verified and vali-
dated. This is done by creating a set of expected values before the actual simulation,
and comparing these to the simulated output. Model verification consists, in large part,
of debugging and is therefore done throughout model development.
In order to build a credible model, the problem must be formulated precisely, as
presented in Appendix C.4 (Law, 2005). When the author initiated the simulation, the
exact problem was not completely understood in its finest detail, which is usually the
case, as agreed by Law (2005). As the problem progressed, greater detail was added
for accuracy.
A subject matter expert (SME) in simulation, the study leader, assisted the author
in gaining a complete understanding of the system to be modeled. It is assumed that
information from SME’s is usually correct.
The author also ensured that the simulation modeled the systems correctly by doing
a structured walk-through, as well as interacting with the staff and other decision
makers at the department. All concepts, changes, and assumptions were documented
throughout the project to ensure that true information was recorded and used for the
simulation.
The author chose to verify and validate the simulation of the current system imple-
mented at the department (Design 1) by comparing its values to true observed values.
It is assumed that if this model is verified and validated, that the data distributions
used in this simulation remain verified for the remaining Designs 2, 3, and 4.
As previously mentioned, an old-fashioned clock card machine was used to calculate
the time in system (TIS) of every customer entering each queue. This actual time in
system was compared to the time in system outputted by the simulation for Design 1,
as shown in Table 5.3.
The actual TIS for the Fines section is not included in the time study, but is realis-
tically estimated at 2.5 minutes, and the simulation agrees. The Licence & Registration
outputs also correlate reasonably. The time in system (TIS) at the Drivers Licences
section requires some explanation. The average observed waiting time is 14 minutes,
whereas the simulated waiting time is 25 minutes. The difference is explained as fol-
lows; the time study to obtain the inter-arrival information and the time in system
51
5.3 Validation and Verification
Table 5.3: Actual vs. Simulated TIS: Design 1
Section Actual Simulated
(minutes)
Fines 2.5 2.42
Licence & Registration 22.8 22.05
Drivers Licence 14.2 25.26
Table 5.4: Actual vs. Simulated Entities Created: Design 1
Section Actual Simulated
(units)
Fines 31 36
Licence & Registration 142 141
Drivers Licence 141 148
(TIS) of each customer was done one week prior to the time study of the service times
at the Drivers Licence server. The service time is independent of the arrival rate,
therefore it is reasonable to use the data from these separate time studies in a single
simulation. However, the observed waiting time is 11 minutes less than the simulation
output because an additional server was used during the time that the time study of
inter-arrivals and waiting time was done. The time study of TIS was done at a partic-
ularly busy period at the Drivers Licence section, leading to the need for an additional
teller. However, this is not the usual case, thus the simulation includes only one server.
It is therefore reasonable that the simulation outputs the time in system (TIS) as 11
minutes longer than the observed waiting time.
The number of entities created by the simulation is also compared to the number
of entities observed, shown in Table 5.4. The actual and simulated results correlate
satisfactorily.
The simulation of Design 1 is therefore verified and validated. Designs 2, 3, and 4
were verified using logical argument, and the assumption that inputs of Design 1 are
valid for the remaining models.
52
5.4 Summary of Simulation Study
5.4 Summary of Simulation Study
This chapter provided the results of the simulations of Designs 1 to 4. It also showed
that Design 4 is the best alternative queue design in terms of average time in system
(TIS), by TOPSIS analysis. Lastly, it described validation and verification of the models
simulated.
The next chapter draws conclusions from the simulation study and makes recom-
mendations to the department with respect to queue design, facility layout and man-
agement.
53
Chapter 6
Conclusions and
Recommendations
This chapter summarises the outcome of the simulation study, recommends a re-
engineered facility layout and then provides managerial advice for implementation.
The Stellenbosch Traffic Department requires much more than only an overhaul of the
queue design, but also an improved management who consider the importance of the
work environment.
6.1 Queueing Model
This project included a simulation of various queue models. Ideas of queue design were
generated from benchmarking and then simulated using real world data obtained by
physical observations. An analysis by TOPSIS shows Design 4 as most optimal between
the current queue model used at department, and the three alternative models.
Design 4 is a single stage, single queue, multiple server model. In this model, all
customers enter a single queue, regardless of the type of transaction to be performed.
The customers are then served on a first-in-first-out (FIFO) basis from this single
queue to the next available of multiple servers who are able to perform all types of
transactions; fines, licences, registrations and drivers’ licences.
The simulation of Design 4 boasts an average time in system of only 4.44 minutes
per customer; a quarter of the current 22 minutes experienced at the department. This
is the most important criteria for improvement at the department as it is the greatest
54
6.2 Facility Layout
Table 6.1: Comparison of Simulation Results of Current- and Proposed Queue Designs
Current Proposed
Performance Measure Design 1 Design 4
TIS (Avg, Minutes) 24.9133 4.4400
CIS (Avg, Number) 21.5247 3.2747
Utilisation (%) 68.5459 63.0218
Customers Not Served (%) 15.5488 1.2903
source of complaints from customers. A summary of the verified simulation results
comparing the currently used queue design (Design 1) and the proposed design (Design
4), are shown in Table 6.1. This outcome shows that the department is in fact not
under staffed, but that staff are under utilised.
This proves the advantage of implementing Design 4. However, in order to im-
plement this queue design, a few structural changes to the building are required, as
detailed in the following section.
6.2 Facility Layout
The proposed layout accommodates Design 4 while making only a few structural
changes, as shown in Figure 6.1. It includes the removal of three existing walls of
“Store 2”, the Drivers Licences cubicle, as well as the Fines cubicle. Refer to Figure 3.1
to compare the proposed- to the existing layout. All transactions are to be processed by
at least six servers in the main building, including two servers stationed at the existing
Enquiries desk.
There is sufficient space to accommodate all entering customers; the simulation of
Design 4 shows a maximum of 27 customers in the system. In contrast, the simulation
of Design 1 shows a maximum of 89 customers in the system. The maximum number
of customers in the system is not given in the tables of Chapter 5, but is deducted
from the simulation output by the author. The Fines cubicle of the current design is
to be converted to a storage room to account for the loss of storage space due to the
demolishment of “Store 2” of the current design. Additional Application Form Stations
are also supplied in the void of the Fines cubicle. A waiting area for eye tests is created,
as well as an area for participants and partners of persons undertaking learners’ licence
55
6.2 Facility Layout
tests, at the previously Drivers Licence section. This allows learners’ licence tests and
eye tests to be conducted every day of the week.
Complete installation of the proposed Design 4 will require that all servers have ac-
cess to the eNatis as well as the OPUS and TCS information systems in order to perform
all transactions. Should the department prefer to have fines processed independently
from the remaining transactions, it is recommended that all fines be processed by En-
quiries, as done at Durbanville Traffic Department.
There are two options for queueing at the waiting area for the eye tests; either the
seating is arranged such that persons sit in the next available seat in chronological order
of arrival (this is the same as a normal queue, except that each person is seated), or
a ticket issuing system can be implemented in which each person entering is issued a
ticket with a customer number, and an automated prompt calls out the next customer
to be directed to the eye test facility. Effective signage in all operational areas are
highly recommended to guide customers through the building.
A company, Qmatic, was approached by the author to discuss the feasibility of using
such a ticketing system. The company director, Mr. Eugene Swanepoel, provided en-
couraging insight. Qmatic has already installed their solutions at Johannesburg Metro
Police Department and Western Cape Department of Transport for public licences in
Bellville. Installations were in progress at Mpumalanga Department of Transport at
the time of correspondence. The Qmatic solution is also part of the “blue print” to
be implemented at traffic departments nationally. This was approved by the National
Department of Transport, but has not been implemented. (Swanepoel, 2012)
Thus far, it has been realised that a more optimal queuing design is advantageous
in reducing the time in system of each customer. It better utilises the servers, and the
flow is more logical and thus easy for customers to understand.
The queue design and facility layout consider only the physical and logical compo-
nents of the system at the department.
The following section focuses on less tactile strategies to improve customer service
at the department; the management and other human capital.
56
6.2 Facility Layout
Enq
uir
ies
All Transactions Servers
Au
tho
risa
tio
nO
ffic
eSt
ore
1
Off
ice
Off
ice
Off
ice
Off
ice
Sto
re 2
Off
ice
Off
ice
Vau
lt
Lear
ner
s Li
cen
ce
Wai
tin
g A
rea
Lear
ner
s’ T
est
Ro
om
(Eve
ry D
ay)
Eye
Test
R
oo
m 1
Eye
Test
R
oo
m 2
Eye
Test
Wai
tin
g A
rea
(Eve
ry D
ay)
Off
ice
Off
ice
Off
ice
Sto
re
ENTR
AN
CE
Fin
es, L
icen
ce &
Reg
istr
atio
n
ENTR
AN
CE
Dri
vers
’ Lic
ence
s
Application Forms Station
Telle
r 6
Telle
r 2
Telle
r3
Enq
uir
esTe
ller
5En
qu
irie
s
Telle
r1
Telle
r3
Au
tho
risa
tio
n
Serv
er
Eye
Test
O
ffic
er 1
Eye
Test
O
ffic
er 2
Off
ices
, Par
ade
Ro
om
, Kit
chen
Enter
Queue
All Tra
nsacti
ons
Ap
plic
atio
n F
orm
s St
atio
n
Application Forms Station
Customer # Call-Out Prompt
“Cu
sto
mer
Nu
mb
er 1
23
, ple
ase
pro
ceed
to
Eye
Tes
t R
oo
m 2
"
Exit
Eye Test
# Is
sue
Authorisation
Eye
Test
Learners Tests
Figure 6.1: Recommended Business Process Flow and Facility Layout
57
6.3 Management
6.3 Management
The introduction to this report mentioned that the department was experiencing a high
occurrence of absenteeism. It was also mentioned in section 2.6.2 that employees at
the department seemed to show little motivation and complained of being over-worked
and stressed. It is suspected that there is a lack of leadership at the department; the
author noticed that the tellers, supervisors and the Administrative Traffic Chief do
not support one another. There is also a functional divide, creating “silos” of sections
(Fines, Licence & Registration, Drivers Licences) with employees refusing to assist one
another. Much commentary along the lines of “It is not my section, so it is not my
problem” was noticed.
In any business, human capital is its most important asset, therefore this is some-
thing which should be given much attention. The time in system is likely to be reduced
by changing the queue design, but in order to deliver excellent customer service, the
employees at the department must be satisfied and comfortable in their work environ-
ment.
This section will focus on providing a recommendation to the department in order
to improve the quality of work delivered by the employees. It includes advice relating
to work motivation, stress management and leadership.
6.3.1 Work Motivation
Various models of motivation reveal that a person requires certain needs to be satisfied
in order to become motivated; specific factors such as physical work condition, payment,
safety, social and belongingness, but also the need to achieve, be recognised, and exercise
authority. There is also consensus that, despite having all their needs satisfied, people
also want to be treated fairly, with an expectation of the value or rewards for every
job done. A major success of theories relating to motivation is the use of goal setting.
(Hitt et al., 2011)
These factors and theories are used to develop a recommendation to improve work
motivation at the department:
Physical Needs The physical work environment at the department is satisfactory.
However, it is recommended to introduce standards of tidiness, cleanliness and
58
6.3 Management
comfort to foster pride within employees. The employees are provided job security
by the mere fact that they are government employees.
Recognition The department makes no room for recognising and rewarding a job well
done. It is recommended that an “Employee of the Month” scheme be used to
give recognition to the top three performers each month. This will also create a
sense of healthy competition amongst the employees. This effectively “infects”
employees with an internal drive to achieve.
Authority The department is hierarchically orientated – this is typical of government
institutions. Without tampering with the major hierarchical structure, it is rec-
ommended to allow all employees to have authority in some area of their work.
This will also require the employees to take responsibility for their work and
reduces the opportunity to shift blame amongst themselves.
Goal Setting Employees of the department do not practise any form of goal setting.
Targets should be set weekly to unite them as a team to work together at achieving
specific numbers of customers served, transactions performed, minimised duration
of cash-ups, performance ratings from customers, etc. All goals should enforce
participation from all employees. It is said by Gryna et al. (2007) that actions
to “motivate” employees are of little value if they are not put in a position of
self-control; provided with knowledge of what they are supposed to do, feedback,
and a means with which to regulate their performance. These must be supplied
by management.
6.3.2 Stress Management
Stress should be managed at an organisational- and individual level. Section 2.6.2.2
provides a few solutions to reduce stress at the work environment, as suggested by Hitt
et al. (2011). The following is also recommended:
Autonomy, Control & Decision Making Hitt et al. (2011) recommends that in-
creasing employees’ autonomy and control while including them in managerial
decision making is also a means of reducing stress. It is recommended that daily
meetings for the servers of all sections be held at the department at 07:30, before
the start of the business day. Inclusion of employees’ opinions and allowing them
59
6.3 Management
to make decisions is a great shortfall experienced at the department. The Chief
Traffic Administrator could be the host of these daily meetings, and must take
cognisance of the servers’ ideas, and allow them to make decisions. This will allow
employees to take ownership of their work and foster inter-relational bonds at the
workplace.
Toxin Handlers It is also recommended that individuals be nominated as “toxin han-
dlers” who can listen and lend advice to employees, even on a personal level. Mr.
Royi should also encourage supervisors to nominate themselves as “toxin han-
dlers” to their immediate staff.
Career Development Currently, the department does not provide opportunity for
advancement. It is recommended that opportunities for employees are created.
Another form of advancement can be introduced by providing related skills train-
ing. Obligatory training on customer service is highly recommended. The staff
currently do not have a customer focus; a crucial aspect to service delivery in a
high customer interaction business such as the department.
Workload Reduction Employees feel that they are overworked. Should the depart-
ment implement the queue system proposed in this report (Design 4), the demand
on servers will be much reduced.
6.3.3 Leadership
It has been noticed that there is a major weakness in the leadership at the department,
which is deemed the responsibility of Mr. Royi. It is with this in mind that the author
recommends the following:
Communication The leader is urged to communicate daily with the servers of all
sections, including his vision for the department; one in which there are no cus-
tomer complaints, employees are focused on the customers’ needs, servers work
as a team, and transactions are processed hassle-free with every employee satis-
fied in their work environment. The leader must also engage with all sections of
the department to gather support and align everyone to a common goal; deliver-
ing excellent service by serving every customer efficiently, effectively and with a
personal touch.
60
6.4 Further Recommendations
Company Culture The work culture at the department is one without pride, esteem,
motivation or focus. It is the responsibility of the leader to foster a culture in
which each individual experiences belongingness and contributes to the company
with integrity, pride, quality and persistence. Above all, there must be a sense of
urgency and initiative on quality throughout all levels of the organisation (Gryna
et al., 2007). The author feels that the department will be able to make the
greatest improvements with respect to service delivery by improving company
culture. It should contribute to reducing absenteeism and increase motivation.
Motivation to Deliver It is noticed by the author that Mr. Royi has personal char-
acteristics in line with being a good leader: integrity, confidence, knowledge of
the industry and cognitive ability, but lacks in enforcing, persisting and demand-
ing performance. There is little “drive” to improve service delivery. The leader
needs to be inspired, and inspire his employees. Here it is recommended that
Mr. Royi do an exchange with the Chief Traffic Administrator at Malmesbury
Traffic Department. This will provide an opportunity for Mr. Royi to experience
a department which works well and should inspire him to achieve the same at the
Stellenbosch department.
Openness to new Solutions The leader is urged to be open to new ideas. These
ideas could stem from employee opinions, customer suggestions, advice from man-
agement, or even recommendations of this report. The only way anything can
change, is if it is allowed to.
6.4 Further Recommendations
The previous sections make the most important recommendations, while the following
section discusses additional recommendations to even further improve service delivery.
Literature in section 2.6.1 discussed the significance of perceived waiting time as
opposed to actual waiting time. In order to create a perception by customers that the
wait in the queue is shorter than it actually is, it is recommended to:
• play calming music throughout the building
• use lighting such that customers are comfortable in their environment
61
6.4 Further Recommendations
• have employees visible to customers in the queue with the supervisor active on
the “floor” and engaging with customers
• allow for social interaction in queues
• provide feedback to customers as to the expected duration until s/he will be
served
A few other recommendations include:
• Credit card facilities should be made available at all traffic departments. Reluc-
tance to implement these facilities due to cash handling fees are an ill-defined
excuse; the cash handling fees imposed by financial institutions can simply be
“built in” to the costing structure of transaction fees by the National Depart-
ment of Transport.
• Operating hours should be modified to allow all transactions to be done from
08:00 – 15:30. Employee working hours are then from 07:30 – 16:00. Servers
should be given permission to leave work once the cash-up is done, and not be
forced to remain at work until 16:00. Benchmarking showed that cashing-up
rarely required more than 30 minutes.
• Lunch breaks should remain as they are; 30 minute lunch break with a 15 minute
tea break. However, it is preferable that servers have their tea while performing
transactions.
• The department should consider using Bluetoothr earpieces for servers at En-
quiries, and the supervisor.
• The use of Eye Test Screening Certificates should be advertised to the public
so as to reduce the workload at the eye test facility and reduce time waited by
customers.
It is important to note that all changes should first be approved by the National
Department of Transport.
62
Chapter 7
Closing Summary
Previous chapters contain, amongst others, literature studies, suggested queuing mod-
els, details on simulation of the models, analysis of the results and a recommendation
to the department. This chapter summarises the final year project. It also shows how
this project contributes to society and that it was a major learning tool for the author.
7.1 Project summary
The primary objective of this project was to reduce time spent waiting in queues at
the Stellenbosch Traffic Department. A secondary objective was to improve overall
customer service by creating a business process which flows naturally, processes trans-
actions efficiently and serves clients without hassle. It was also a priority to make use
of Industrial Engineering tools, such as queuing theory, simulation and other principles.
The author studied literature on queuing theory, and self-studied simulation and the
Simio software package with the aid of the study leader. Chapter 3 explored the oper-
ations of three local traffic departments in comparison to the Stellenbosch department.
This was used to suggest alternative queue models to be simulated – the results of
which are analysed in Chapter 5. Finally, a three dimensional recommendation is given
which includes a near-optimal queue model, improved facility layout, and managerial
advice for improved customer service.
In the interest of the examiner, Appendix D provides an extract of meetings with
the study leader, as well as a summary time sheet.
63
7.2 Future Work
7.2 Future Work
The scheduling of lunch times is self-decided at all traffic departments. It would be
advantageous to develop a method in which to determine optimal times at which servers
should go on lunch. The author would have liked to have been able to simulate such
a problem and find a near-optimal solution using “OptQuest”; an optimizer in Simio.
Unfortunately, this could not be done as input data was calendar independent. An
Excel analysis of arrival data collected over a one week period also showed that there
is little predictability in arrivals; the sum of data from one week resulted in a uniform
distribution. However, the author is of the opinion that there is opportunity for such
a solution to be researched.
Further research could also include identifying unexpected effects of the implemen-
tation of the recommendations made in this report.
7.3 Contribution to Society
Many traffic departments across South Africa deliver unsatisfactory service. The Stel-
lenbosch Traffic Department is one not to be excluded in terms of customer service and
time waited in queues. It has caused much frustration to the residents of Stellenbosch
and criticism directed at the department’s management.
The simulations developed and the recommendations made by this report should
enable the Stellenbosch Traffic Department to deliver all services effectively. This could
encourage more road users to renew licences, roadworthy vehicles, and pay fines – all
of which contribute to creating a conforming society, increasing revenue for the state,
and allowing for safer cars on South African roads.
7.4 Lessons Learnt
Performing the final year project was one which has taught and enabled the author on
various levels. It is difficult to describe every enrichment in only one paragraph. A
major realisation was that of the author’s independent learning ability. A reflection of
a few key lessons learnt are listed:
• Everything always takes longer than expected.
64
7.5 Denouement
• Assumptions can be the master of all faults, but valuable in finding approximate
outcomes.
• There is never a perfect solution – it can always be done better.
• Conversation with persons unrelated to the problem being researched often results
in innovative ideas being realised.
• American vs. South African language conventions are a source of irritation.
• Simio, used for simulation in this project, was self-studied. The author had had
no prior experience with any sort of simulation.
• LATEX, in combination with WinEdt6, was used for typesetting as prescribed by
the study leader. Yet another invaluable tool was added to the author’s skill set.
The author realised that there is still much to learn and feels that this project has
provided equipment for a successful future in Industrial Engineering.
7.5 Denouement
This chapter provided a summary of the project and described items for future research.
This project’s contribution to society is briefly described, as well a few key lessons learnt
by the author.
The author hopes that you have had an enjoyable read.
65
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69
Appendix A
Supporting Information
This appendix contains newspaper articles of complaints and reactions directed at the
Stellenbosch Traffic Department. It also contains activity diagrams drawn by the author
in understanding the process flow of the department, and the project plan as updated
continuously by the author during execution of this project. The template used in
server self-time study is also included in this appendix.
A.1 Newspaper Articles
Figure A.1: “Rotten service detrimental to the economy.”(Eikestad News, 2012)
70
A.1 Newspaper Articles
Figure A.2: “Service doesn’t exist.”(Eikestad News, 2012)
71
A.1 Newspaper Articles
Figure A.3: “Officers react to complaints.”(Eikestad News, 2012)
72
A.2 Project Plan
A.2 Project Plan
Various due dates were identified and tasks scheduled to meet these, as in Figure A.4
(overleaf). The project was executed in order of “nearest due date”. The Gantt chart
was used to give the author an indication of progress of the final year project, and
to prioritize activities. It was updated continuously as changes to the project were
realised.
73
A.2 Project Plan
IDT
ask N
am
eD
ura
tio
nS
tart
Fin
ish
1Topic Reg
istration
1 day
Feb
ruary 24
Feb
ruary 24
2Project Proposa
l3
Literature Research: Simulation &
Arena
4 da
ys?
Feb
ruary 24
Feb
ruary 29
4Library Resea
rch: Related
topics
8 da
ys?
March 07
March 16
5Plann
ing & Study Lea
der Mee
tings
3 da
ys?
March 15
March 19
6Project Plan
1 da
y?March 19
March 19
7Problem
Statemen
t from Mr. Royi
1 da
y?March 14
March 14
8Report W
riting
2 da
ysMarch 20
March 21
9Progress
Rep
ort
10
Literature Research: Que
uing
&
Simulation
96 days
April 24
Aug
ust 3
0
11
Literature Research : P
erf M
easures,
Fac Layou
t13
2 da
ysApril 24
Octob
er 18
12
Literature: LaT
eX13
2 da
ys?
April 25
Octob
er 19
13
Activity Cha
rting
3 da
ys?
April 26
April 30
14
Que
uing
The
ory Ana
lysis
5 da
ysAug
ust 3
1September 06
15
Report W
riting
2 da
ys?
October 22
Octob
er 23
16
Exa
ms
15 day
s?May
21
June 08
17
Holid
ay W
ork
18
Sho
rt Cou
rse on Simio/Simulation
1 da
yJune
11
June
11
19
Time Study at D
epartmen
t21
days
June
11
July 06
20
Ben
chmarking
5 da
ysJuly 02
July 06
21
Simulation
6 da
ys?
July 23
July 30
22
Update Report
5 da
ys?
October 19
Octob
er 25
23
70% Draft
24
Further simulation
2 da
ys?
Aug
ust 1
8Aug
ust 2
025
Add
ition
al data requ
ired
5 da
ys?
Aug
ust 2
0Aug
ust 2
426
Advice from
Lan
guage Centre
1 da
y?Aug
ust 2
4Aug
ust 2
427
Improve 70
% Rep
ort
3 da
ysAug
ust 2
3Aug
ust 2
728
Pee
r Rev
iews
5 day
s?August 27
August 31
29
Prelim
inary Exa
m Copy
30
Fee
dback ad
justmen
ts15
days?Sep
tembe
r 11
September 30
31
Ben
chmarking
1 da
y?Sep
tembe
r 17
September 17
32
Add
. Simulation
3 da
ys?Sep
tembe
r 19
September 22
33
Facility Design
2 da
ys?Sep
tembe
r 23
September 24
34
TOPSIS
2 da
ys?Sep
tembe
r 27
September 30
35
Edit R
eport
1 da
y?October 30
Octob
er 30
36
Final Rep
ort
37
Simulation Stats Ana
lysis
8 da
ys?
October 01
Octob
er 10
38
TOPSIS 75th %ile
6 da
ys?
October 08
Octob
er 15
39
Edit R
eport
16 days?
October 16Novem
ber 06
40
Exa
ms
15 day
s?October 29Nove
mber 16
41
Summary Slid
e2 day
s?Nove
mber 16Nove
mber 19
No
vJan
Mar
May
Jul
Sep
Nov
1st
Qua
rte
r3rd
Qua
rter
1
Task
Split
Mile
sto
ne
Sum
mary
Pro
ject
Su
mm
ary
Exte
rna
l T
asks
Exte
rnal M
ilesto
ne
Inactive T
ask
Inactive M
ilesto
ne
Ina
ctive
Su
mm
ary
Ma
nua
l T
ask
Dura
tion
-only
Man
ual S
um
mary
Ro
llup
Man
ual S
um
mary
Sta
rt-o
nly
Fin
ish-o
nly
Pro
gre
ss
De
adlin
e
Page
1
Pro
ject:
Skri
psie
Pla
nnin
gD
ate
: O
cto
ber
20
Figure A.4: Planned Tasks and Deadlines for the Project.
74
A.3 Time Study Template
A.3 Time Study Template
Sect
ion
1A
uth
ori
sati
on
2Fi
nes
3Li
cen
ces
4R
egis
trat
ion
& L
icen
sin
g(R
oad
wo
rth
y/Fi
nes
/Lic
ence
s/R
egis
trat
ion
&Li
cen
sin
g)
Dat
ed
dm
my
yy
yD
ay
Tota
l
8am
-9
am1
23
45
67
89
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
9am
-1
0am
12
34
56
78
91
01
11
21
31
41
51
61
71
81
92
02
12
22
32
42
52
62
72
82
93
0
10
am-
11
am1
23
45
67
89
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
11
am-
12
am1
23
45
67
89
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
12
am-
1p
m1
23
45
67
89
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
1p
m-
2p
m1
23
45
67
89
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
2p
m-
3p
m1
23
45
67
89
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
3p
m-
3.3
0p
m1
23
45
67
89
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Co
mm
ents
: Fee
l fre
e to
co
nve
y an
y su
gges
tio
ns
you
hav
e to
imp
rove
th
e se
rvic
e an
d f
low
of
peo
ple
at
the
Stel
len
bo
sch
Tra
ffic
Dep
artm
ent
her
e.
You
r co
mm
ents
will
rem
ain
an
on
ymo
us!
Inst
ruct
ion
s
Ple
ase
com
ple
te t
he
form
sta
tin
g th
e ap
pro
pri
ate
sect
ion
(R
oad
wo
rth
y/Fi
nes
/Lic
ensi
ng/
Lice
nce
&R
egis
trat
ion
) w
ith
th
e d
ate
and
day
.
Ple
ase
tick
th
e ap
pro
pri
ate
bo
x ea
ch t
ime
a cu
sto
mer
is s
erve
d b
y yo
u a
s a
telle
r. Y
ou
r n
ame
do
es n
ot
app
ear
on
th
e fo
rm, a
nd
will
rem
ain
an
on
ymo
us.
This
info
rmat
ion
will
on
ly b
e u
sed
to
det
erm
ine
the
cap
acit
y o
f th
e tr
affi
c d
epar
tmen
t, N
OT
to m
on
ito
r yo
ur
per
form
ance
- w
e kn
ow
th
at y
ou
wo
rk e
xtre
mel
y h
ard
:)
for
Lugu
en G
ass
Tim
e S
tud
y: H
ou
rly
Cu
sto
me
r V
olu
me
at
Telle
rs (
Serv
ice
Tim
e)
Nu
mb
er o
f C
ust
om
ers
Tota
l
Sect
ion
nu
mb
er 1
or
2 o
r 3
or
4 -
->
Mo
n/T
ues
/Wed
/Th
urs
/Fri
/Sat
Nu
mb
er o
f R
OA
DW
OR
THIE
SN
um
ber
of
tran
sact
ion
s re
qu
irin
g A
UTH
OR
ISA
TIO
N
Figure A.5: Time Study Template for Servers
75
Appendix B
Queuing Models
B.1 Alternative Queuing Models
This section attempts to convince the reader that alternative queuing models are worth
considering to improve operational flow at the department. Two basic queuing models
will be explored in this section. The first model is that which is currently implemented
at the department; where clients are required to enter various (multiple) queues, de-
pendant on the type of transaction to be performed: fines, licence and registration, or
drivers licence transactions. The second model goes to show a different example where
customers need only enter a single queue, regardless of the type of transaction.
The following examples calculate the effect of queue design on customer waiting
time and server utilisation. It aims to convince the reader that considering alternative
queue designs is worthwhile.
B.1.1 Multiple Servers, Multiple Queues
This section refers to the current layout of the Stellenbosch Traffic Department in which
a client stands in one queue to pay a fine, another queue to renew a license, or another
queue to register a vehicle, as in Figure 4.1.
This model is an M/M/1 described by the Kendall Lee notation where the inter-
arrival and service times are assumed to be exponential. Winston (2004) explains that
an exponential distribution of arrival and service times is reasonably assumed when
no specific data of the nature of the inter-arrival and service times is available. The
capacity of the queue and its discipline are not of importance for the purpose of this
example.
76
B.1 Alternative Queuing Models
Queuing theory relating to this type of model and the model in the next section can
be found in most related textbooks, such as Winston (2004) and Gross et al. (2008).
The following symbols are fundamental to queuing theory:
λ Average arrival rate of clients (clients per time unit)
µ Average service rate of clients (clients per time unit)
ρ Probability (or proportion of time) server is in service, or workload rate of server,
or traffic intensity
The probability, ρ, is a ratio described as:
ρ = λ/µ
The specific formulae for the M/M/1 queuing model are given below. The proba-
bility that the server is idle (not in service) is
1− ρ.
The mean number of customers in the system is given by L, where
L = ρ/(1− ρ).
By Little’s Law of section 2.1.1, the average time a customer spends in the system,
that is waiting in the queue and being served, is given by W :
W = L/λ
= (ρ/1− ρ)/λ
= ρλ/(1− ρ)
A multiple queue example is presented to give the reader an idea of the effects of
such a queuing system on the time a customer spends in the system, and the utilization
of the servers. For this reason the arrival and service times are assumed.
Example 1 — Multiple Queues, Multiple Servers Assume that 45 customers en-
ter the traffic department each hour and that a server takes 3 minutes to serve a
client, on average. The inter-arrival and service times are reasonably assumed to
be exponentially distributed (Winston, 2004). There are three separate queues
handling the transactions.
77
B.1 Alternative Queuing Models
From this, it can be noted that
λ = 45/3 = 15 clients/hr per queue and
µ = 60/3 = 20 clients/hr per queue
Therefore,
ρ = λ/µ
= 15/20
= 0.75
The proportion of idle time of each server is then described by
1− ρ = 1− 0.75
= 0.25
This means that the server is idle approximately 25% of the time.
The average time the customer spends in the system:
W = L/λ
= (ρ/1− ρ)/λ
= ρ/[(λ)(1− ρ)]
= 0.75/[(15)(1− 0.75)]
= 0.2 hours
= 12 minutes
B.1.2 Multiple Servers, Single Queue
This section introduces the reader to a queueing model in which clients stand in one
single queue to be served, regardless of the transaction type. This model illustrates a
possible alternative solution to the queuing issue at the Stellenbosch department. In
this queueing model, the client stands in one queue in which all transactions can be
done; a fine can be paid, or a license renewed, etc. See Figure 4.4.
This model is an M/M/S according to the Kendall Lee notation where the inter-
arrival and service times are assumed to be exponential and there are S servers serving
the queue. Again, this is reasonably assumed (Winston, 2004).
78
B.1 Alternative Queuing Models
Table B.1: P (j ≥ S) for the M/M/s Queueing System
ρ S = 2 S = 3 S = 4 S = 5 S = 6 S = 7
.10 .02 .00 .00 .00 .00 .00
.20 .07 .02 .00 .00 .00 .00
.30 .14 .17 .04 .02 .01 .00
.40 .23 .14 .09 .06 .04 .03
.50 .33 .24 .17 .13 .10 .08
.55 .39 .29 .23 .18 .14 .11
.60 .45 .35 .29 .24 .20 .17
.65 .51 .42 .35 .30 .26 .21
.70 .57 .51 .43 .38 .34 .30.75 .64 .57 .51 .46 .42 .39.80 .71 .65 .60 .55 .52 .49.85 .78 .73 .69 .65 .61 .60.90 .85 .83 .79 .76 .74 .72.95 .92 .91 .89 .88 .87 .85
(Winston, 2004)
From this type of queueing model, the probability that the server is idle (not in
service) is calculated using a steady-state probability. A steady-state probability is one
in which the probability is calculated as though the queueing model runs to infinity and
reaches a steady-state where values remain approximately constant. The steady-state
probability is represented by πj where there are j entities in the system.
The following formulae are applicable:
π0 = S!P (j ≥ S)(1− ρ)/(Sρ)2 (B.1)
πi = (Sρ)iπ0/i! (B.2)
i = 1, 2, ..., j.
S refers to the number of servers in the system, and the values for P(j ≥ S) can be
found in Table B.1.
The probability that a server is idle is the same as the probability that there is no
entity at the server. For this queuing system in which there are three servers (S=3),
the probability that a server is idle is equal to the probability that there is no entity in
the queue plus the probability that if there is one entity in the queue, that one of the
other two available servers will serve that entity, plus the probability that if there are
79
B.1 Alternative Queuing Models
only two entities in the queue, that they will be served by the other two servers. This
is illustrated mathematically as follows:
P (idle) = π0 +2
3π1 +
1
3π2
Example 2 — Single Queue, Multiple Servers Assume that 45 customers enter
the traffic department each hour and that a server takes 3 minutes to serve a client,
on average. The inter-arrival and service times are assumed to be exponentially
distributed. This is the same scenario as Example 1, except that there is only
one queue, but which handles all types of transactions.
From this, it can be said that λ = 45 clients/hr and µ = 60 clients/hr.
Therefore,
ρ = λ/µ
=45
60
Now, calculating π0, π1, and π2 using (B.1) and (B.2):
π0 = S!P (j ≥ S)(1− ρ)/(Sρ)2
= 3!(0.57)(1− 45/60)/(3× 45
60)2
=38
225
π1 = (Sρ)1π0/1!
= 3(45
60)(
38
225)
=19
50
π2 = (Sρ)2π0/2!
= [(3× 45
60)2(
38
225)]/2
=171
400
80
B.1 Alternative Queuing Models
Therefore,
P (idle) = π0 +2
3π1 +
1
3π2
=38
225+ (
2
3)(
19
50) + (
1
3)(
171
400)
= 0.5672
This means that each server is idle approximately 56.72% of the time.
The average length of the queue for this example is given by:
Lq = P (0 ≥ S)ρ/1− ρ
= (0.57)(45
60)/1− (
45
60)
= 1.71 customers
In order to calculate the average time the customer spends in the system, the average
number of customers in the system is required. The average number of customers in
the system is equal to the number in the queue, (Lq), and the number of customers in
service, (λ/µ).
L = Lq +λ
µ
= 1.71 +45
60= 2.46 customers
From Little’s Law, one can calculate the average time the customer spends in the
system:
W = L/λ
= 2.46/45
= 0.0546 hours
= 3.28 minutes
A summary of this analysis is provided in Section 4.2.
81
Appendix C
Simulation Model Notes
This appendix contains information relating to the simulation of the queue designs. It
includes a functional specification, assumptions of-, and describes the models developed
for simulation. Lastly, it contains a summary of the distributions fitted to data obtained
by physical time studies.
C.1 Functional Specification
It is recommended by Kelton et al. (2010) to create a functional specification early in
the simulation modeling process. It is said to assist the modeler in conceptualising and
translating information pertaining to the simulation, details the system by considering
the process flow, resources, and operations involved, and identifies which data inputs
and outputs are required (Kelton et al., 2010). The following sub-sections detail the
functional specification.
C.1.1 Operational Sections
The Stellenbosch Traffic Department is modularised into specific areas of transactions.
Fines, Licence & Registration, and Drivers Licence sections operate independantly, and
perform only specific transactions.
C.1.2 Servers
Clients who enter the department compete for service from servers or tellers of the
department at a specific section. The servers complete transactions at a certain service
rate; the time it takes to serve a customer.
82
C.2 Input and Output Data
C.1.3 Customers
Customers arrive at the department requiring to perform a certain type of transaction,
such as paying a fine, renewing a license, or applying for a roadworthy certificate.
Customers arrive independently, and sometimes in bulk.
C.1.4 Transactions
Customers have specific transactions which they would like performed. Each transac-
tion type is unique, and associated with a service time.
C.1.5 Flow
The physical layout and operational flow of queues consider the way in which customers
are expected to queue and how servers are distributed between sections, as well as the
transaction types performed by each server.
C.1.6 Schedules
The Stellenbosch Traffic Department operates from 08:00 – 15:30. Servers are entitled
to a 30 minute lunch break after at most 5 hours of continuous work, and a 15 minute
tea break.
C.2 Input and Output Data
Considering each design to be simulated, as introduced in section 4.2, each data input
is identified. The two main data inputs to the simulation are the customer arrivals,
and the service rates of the servers.
C.2.1 Input Data
The input data is acquired by physical time-motion studies of customer arrivals, server
service rates, and other observations over a three week period from 18 June to 6 July
2012. The time studies are conducted in collaboration with Ms. Renette de Villiers, a
third-year Mechanical Engineering student at Stellenbosch University.
A description of which data, and how it was collected, is described:
83
C.2 Input and Output Data
Customer Arrivals As a customer entered a queue at the department, the time at
which the customer arrived was recorded using Microsoft Excel’s “time stamp”
function. Bulk arrivals were also noted. The time study was done at each opera-
tional section (Fines, Licence & Registration, Drivers Licences) for a week, each;
totalling a three week physical time study period.
Server Service Rate Also using Microsoft Excel, the time at which a server began
a transaction and the termination of a transaction was recorded. The difference
between the times gives the service time for each transaction. This was done
for all servers for a full 712 hour shift. At first a time study template was given
to each server on which the server was to tally the number of customers served
per hour, as discussed in 2.2.2. This concept originated after the author noticed
such a template being used by the South African Post Office. The template is
included in Appendix A.3. Unfortunately, this self-time study method failed as
the tellers were reluctant to cooperate, and often forgot to tally the customers.
A time study performed by the author soon followed.
Transaction Segment Times In the same way server service times were studied, the
times for each segment of a transaction were recorded. This provided the times
for Design 2 in which each server has only one function: application, payment, or
issuance. Each transaction was divided into these three segments at each section.
Time in System The time at which a customer entered the queue was stamped onto
a clock card using an old-fashioned clock-card machine. As the customer exited
the system, after having been served, the card was once again stamped to de-
termine the actual time the customer spent in the system. This is also used for
validation and verification of the simulation of Design 1: the current layout of
the Stellenbosch Traffic Department.
ARENA, a simulation package, offers an “Input Analyzer” which was used to fit distri-
butions to the physical time study data. To ensure that distributions are statistically
sound, only distributions with p-values > 0.05 were used. In the event that no such
distribution could be found, an empirical distribution was used. A summary of data
distributions used in the simulations is supplied in Appendix C.5.
84
C.3 Assumptions
C.2.2 Output Data
In order to validate the simulation, it is required to have the following output statistics:
• Number of customers entering the system (entities created)
• Time in system (TIS)
• Server processing time
In order to make an informed decision on which design (1, 2, 3, or 4) is best, the
following is required:
• Time in system (TIS)
• Number of customers in system (CIS)
• Utilisation of resources (the servers)
• Percentage of customers not served
Output data is assumed to be statistically viable since 1000 replications of each
experiment are performed. This ensures that h-values are minimised, resulting in nar-
rowed confidence intervals.
C.3 Assumptions
In developing the simulations it is necessary to make some simplifying assumptions,
but which do not compromise the integrity of the simulation. Assumptions are only
made where they intuitively have little or no effect on the accuracy of the simulation.
These include:
Bulk Arrivals Each bulk arrival is noted as being an arrival of exactly two customers,
no more. Effects of balking, reneging, and jockeying are ignored on advice from
the study leader (Bekker, 2012b).
Data Distributions Distribution curves fitted to the measured data are assumed to
be reasonable since p-values of each are well above 0.5, and have expected values
within 5% of the actual observed values. All distributions are assumed to be
independent.
85
C.4 Model Experiments
Service Time The service rate of the tellers is assumed to be representative of any
day, not only the day on which the observations were made. This also implies
that the study ignores the Hawthorne effect; a change in natural occurrences due
to the mere physical presence of the author doing a time study.
C.4 Model Experiments
The previous sections discussed functional specifications of the simulation models,
which data is required, and described the assumptions to put the simulation in context
for the reader.
The simulation models built for this project consist of the designs discussed in sec-
tion 4.2 and are “built” in separate models using a simulation package, Simio. Each
model is described by one common process; a customer arrives at the Traffic Depart-
ment, enters at the back of a queue, is served in a first-in-first-out (FIFO) fashion by
a server, and exits the system. The difference between the models is that of the layout
of the queues, the nature of entering the queue, and the nature of service.
Customers performing Licence & Registration type transactions are also subject
to authorisation at another step in the serving process. The authorisation service
time is included in all simulations. Due to the fact that only approximately 10% of
all customers requiring to perform a Licence & Registration type transactions require
authorisation, a large variation in Authorisation service rates is realised between the
models (or designs). To ensure that comparison between designs is fair, it was decided
to use the average service time of 9.18 minutes as a mean service rate. All customers
who require authorisation after being served by a teller then re-enter the queue. They
re-enter at the front of the queue, rather than at the back. A customer only enters at
the back upon first entry of the queue.
Further details of each model experiment and respective outcomes are presented in
the following subsections.
C.4.1 Design 1 — Single Stage, Multiple Queue, Single and MultipleServer
This model represents the current queue design at the department, as in Figure 4.1.
A customer entering the department is required to enter a specific queue, depending
on the type of transaction s/he would like to perform. To pay a fine the customer is
86
C.4 Model Experiments
obligated to enter the queue at the Fines section, and to renew a drivers’ licence the
customer must enter a separate queue at the Drivers Licence section. This model is
necessary to be simulated as it forms part of the reference point for verification and for
comparison to measure the success of the proposed designs 2, 3 and 4.
Customers who intend on performing a Licence & Registration type transaction
assemble in one queue and are then distributed to the next available of two servers.
On the other hand, customers at the Fines- or Drivers Licences section form a queue
directly at a single server.
C.4.2 Design 2 — Single Stage, Multiple Queue, Single Server
This is the first of three proposed alternative queueing designs. All customers can
choose to enter any queue and can perform any transaction at the server. Refer to
Figure 4.2.
The model is simulated such that a customer will choose the shortest queue; one
with the least number of entities in service and waiting for service. However, it must
be noted that it is unlikely that customers will first make an accurate calculation of the
number of customers in each queue before they decide to enter one. This implies that
the waiting time in reality is likely to be larger than that outputted by the simulation.
Again, it is approximated that 10% of all customers performing Licence & Registration
type transactions require authorisation after being served, and then have to re-enter
the queue.
C.4.3 Design 3 — Multiple Stage, Single Queue, Single Server
Each segment of a transaction is assigned to a separate server. A customer enters
the queue and waits his/her turn to be served by the first server, the Applications
server. Here the customer hands over the documentation to the server and any other
representation required. Once the Application server has completed the application
segment of the transaction, the customer moves to the next server. A customer can
only move to the next server to perform the next segment of the transaction once the
next server is available. This is similar to the queue of a drive-through restaurant.
Now, at the Payment server, the customer is informed of the amount payable, and
pays. Once the payment is confirmed, the receipt is given to the customer, and s/he
again moves to the next (Issuing) server and collects the final document or item. Ten
87
C.5 Data Distributions Summary
percent of all customers performing a Licence & Registration type transaction are first
routed to the Authorisation server, before moving to the Issuing server.
C.4.4 Design 4 — Single Stage, Single Queue, Multiple Server
Customers all enter into a single queue, regardless of the type of transaction they
would like to perform, and can be served by one of multiple servers – which ever
server is available next (see Figure 4.4). The customer enters at the back of the queue.
Customers go to the next available server once they are at the front of the queue. Again,
the need for authorisation of Licence & Registration type transactions is considered.
C.5 Data Distributions Summary
A summary of all distributions fitted, using ARENA, to data of the physical time
studies, are shown in Table C.1 (overleaf).
88
C.5 Data Distributions Summary
Tab
leC
.1:
Su
mm
ary
of(F
itte
d)
Tim
eS
tudy
Dat
aD
istr
ibu
tion
s
Day/Segm
ent
Mean
Bulk
Arrivals
Distrib
ution
(Arena)
p-valu
eExpecte
dValu
e
Fin
es
Inte
rarr
ival
Tim
eM
on
18
Ju
ne
15.4
583
6/31
0.5
+G
am
ma(1
2.7
,1.1
8)*
*0.0
515.4
860
Tu
e19
Ju
ne
12.5
806
1/32
0.5
+E
xp
on
enti
al(
12.1
)0.1
25
12.6
000
Wed
20
Ju
ne
7.4
211
12/79
0.5
+G
am
ma(5
.67,1
.22)*
*0.5
36
7.4
174
Thu
rs21
Ju
ne
9.6
889
7/53
0.5
+G
am
ma(8
.09,
1.1
4)*
*0.4
55
9.7
226
Fri
22
Ju
ne
10.0
476
3/46
0.5
+W
eib
ull(9
.39,0
.964)*
*0.1
69
10.0
400
Ser
vic
eT
ime
Fri
29
Ju
ne
1.9
427
Gam
ma(0
.93,2
.09)*
*>
0.1
51.9
437
Seg
men
ted
Ser
vic
eT
ime
Ap
plica
tion
0.9
615
Exp
on
enti
al(
0.9
61)
>0.1
50.9
610
Paym
ent
0.6
156
Wei
bu
ll(0
.601,0
.953)*
*>
0.1
50.6
140
Issu
an
ce0.3
656
0.0
1+
Gam
ma(0
.169,
2.1
)**
>0.1
50.3
649
Licence&
Registration
Inte
rarr
ival
Tim
eM
on
18
Ju
ne
3.9
000
31/142
0.5
+W
eib
ull(3
.61,
1.1
8)*
*>
0.7
53.9
100
Tu
e19
Ju
ne
3.3
111
56/192
0.5
+G
am
ma(1
.75,
1.6
1)*
*0.0
51
3.3
175
Wed
20
Ju
ne
3.1
972
47/190
0.5
+E
xp
on
enti
al(
2.7
)0.0
75
3.2
000
Thu
rs21
Ju
ne
2.9
045
45/203
0.5
+11*B
eta(0
.926,
3.3
1)
0.5
36
2.9
046
Fri
22
Ju
ne
2.9
530
30/180
0.5
+W
eib
ull(2
.62,
1.1
9)*
*0.6
41
2.9
600
Ser
vic
eT
ime
Tu
e26
Ju
ne
3.9
640
Wei
bu
ll(4
.27,
1.1
7)*
*0.4
44.0
400
Seg
men
ted
Ser
vic
eT
ime
Ap
plica
tion
2.4
962
11*B
eta(0
.574,
1.9
6)
0.1
36
2.4
917
Paym
ent
0.7
474
Exp
on
enti
al
(0.7
47)
0.6
55
0.7
470
Issu
an
ce0.7
211
Exp
on
enti
al
(0.7
21)
0.0
712
0.7
210
DriversLicences
Inte
rarr
ival
Tim
eM
on
2Ju
ly3.5
378
22/141
0.5
+11*B
eta(0
.926,
2.4
3)
0.7
45
3.5
352
Tu
e3
Ju
ly3.6
583
10/130
0.5
+W
eib
ull(3
.38,
1.2
2)*
*0.5
42
3.6
600
Wed
4Ju
lyL
earn
ers
Lic
ence
sO
nly
(Wed
nes
days)
Thu
rs5
Ju
ly3.7
288
15/133
0.5
+W
eib
ull(3
.44,
1.1
9)*
*0.2
97
3.7
400
Fri
6Ju
ly3.7
701
6/93
0.5
+E
xp
on
enti
al(
3.2
7)
0.1
13.7
700
Ser
vic
eT
ime
Thu
rs28
Ju
ne
3.2
330
1.1
6+
Gam
ma(0
.409,
5.0
7)*
*0.6
99
3.2
336
89
C.5 Data Distributions Summary
Day/Segm
ent
Mean
Bulk
Arrivals
Distrib
ution
(Arena)
p-valu
eExpecte
dValu
eS
egm
ente
dS
ervic
eT
ime
Ap
plica
tion
1.8
900
0.3
2+
Gam
ma(0
.295,5
.32)*
*0.3
57
1.8
894
Paym
ent
0.2
660
Em
pir
ical
sin
ce¡0
.005
Not
Su
itab
le(1
/12,3
/77,1
3/30,1
0/11,4
7/60,7
4/77,1
7/15,7
5/77,8
9/60,7
6/77,1
1/6,7
6/77,1
31/60,7
6/77,3
8/15,1
)Is
suan
ce1.0
750
Gam
ma(0
.491,2
.19)*
*0.0
931
1.0
753
LearnersLicences
Inte
rarr
ival
Tim
eW
ed4
Ju
ly8.2
917
35/83
0.5
+W
eib
ull(5
.73,0
.678)*
*0.1
72
7.9
800
Ser
vic
eT
ime
Wed
27
Ju
ne
2.2
460
Em
pir
ical
sin
ce¡0
.005
Not
Su
itab
le(5
3/30,1
/35,7
91/360,1
7/35,4
73/180,3
1/35,3
67/120,3
4/35,1
57/45,3
4/35,1
411/360,3
4/35,8
7/21,1
)
Auth
orisation
Inte
rarr
ival
Tim
eJu
ne
Ass
um
pti
on
—10%
of
Lic
ence
&R
egis
trati
on
arr
ivals
Ser
vic
eT
ime
Fri
29
Ju
ne
9.1
8N
ot
Su
itab
le.
Con
stant
serv
ice
tim
een
sure
sfa
irco
mp
ari
son
of
mod
els
9.1
800
**
Ind
icate
sth
at
the
para
met
erm
ust
be
inver
ted
for
use
inS
imio
90
C.6 TOPSIS Calculations
C.6 TOPSIS Calculations
Table C.2: TOPSIS Analysis of 75th Percentile Results
Performance Measures Matrixvj TIS (Avg, Minutes) CIS (Avg, Number) Utilisation (%) Customers Not Served (%)
Design 1 24.9133 21.5247 68.5459 15.5488Design 2 4.5860 3.3588 62.9562 1.2739Design 3 75.9809 55.0176 59.9900 31.4465Design 4 4.4400 3.2747 63.0218 1.2903
Normalised MatrixPmax(vj) 75.9809 55.0176 68.5459 31.4465
rij = 0.3279 0.3912 1.0000 0.49450.0604 0.0610 0.9185 0.04051.0000 1.0000 0.8752 1.00000.0584 0.0595 0.9194 0.0410
Weighted Normalised MatrixWeighting 0.7500 0.0833 0.0833 0.0833
Tij = 0.2459 0.0326 0.0833 0.04120.0453 0.0051 0.0765 0.00340.7500 0.0833 0.0729 0.08330.0438 0.0050 0.0766 0.0034
TIS (Avg, Minutes) CIS (Avg, Number) Utilisation (%) Customers Not Served (%)(Cost) (Cost) (Benefit) (Cost)
Ab = 0.0438 0.0050 0.0729 0.0034Aw = 0.7500 0.0833 0.0833 0.0833
Table C.3: TOPSIS Analysis of 75th Percentile Results (continued)
Model dib diw Sib
Design 1 0.20771 0.50838 0.7099Design 2 0.00389 0.71359 0.9946Design 3 0.71499 0.01040 0.0143Design 4 0.00369 0.71502 0.9949
91
Appendix D
Administration of theFinal Year Project
This appendix provides the reader with an extract of minutes of meetings held between
the author and the study leader, as well as a summary time sheet detailing the activities
and durations of tasks completed in creating this final year project. The agendas and
time sheets illustrate the author’s independent project management ability.
D.1 Meetings with the Study Leader
It was recommended by the study leader that agendas be drawn up for meetings to
ensure that they are effective, and also to serve as an archive for ideas and advice given.
It was said to be used in the event of any disputes during the execution of the project.
An extract of of meeting minutes is supplied. The reader is, however, invited to request
the complete collection of meeting minutes; the author has this filed.
92
D.1 Meetings with the Study Leader
Figure D.1: Extract of Meeting Minutes: Meeting 6.
93
D.2 Summary Time Sheet
D.2 Summary Time Sheet
The author continuously recorded the activities and durations contributing to this final
year report, a summary of which is shown in Figure D.2. Kindly request the complete
breakdown of activities from the author, should it be required.
Name Luguen Gass Total Hours 319.8333333
Student Number 15771598 Hours Per Month 35.53703704
Hours Per Term 79.95833333
Hours (1st Semester) 62.5
June/July Holiday 108
Hours (2nd Semester) 149.3333333
Dissertation Time Sheet | SUMMARY
Figure D.2: Summary Time Sheet as on 21 October 2012.
94