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Data-Based Service Networks:A Research Framework for
Asymptotic Inference, Analysis & Controlof Service Systems
Avi Mandelbaum
Technion, Haifa, Israel
http://ie.technion.ac.il/serveng
INFORMS Beijing, June 2012
1 1
Research Partners� Students:
Aldor∗, Baron∗, Carmeli, Feldman∗, Garnett∗, Gurvich∗, Huang,Khudiakov∗, Maman∗, Marmor∗, Reich, Rosenshmidt∗, Shaikhet∗,Senderovic, Tseytlin∗, Yom-Tov∗, Yuviler, Zaied, Zeltyn∗, Zychlinski,Zohar∗, Zviran∗, . . .
� Theory:Armony, Atar, Gurvich, Jelenkovic, Kaspi, Massey, Momcilovic,Reiman, Shimkin, Stolyar, Wasserkrug, Whitt, Zeltyn, . . .
� Industry:Mizrahi Bank (A. Cohen, U. Yonissi), Rambam Hospital (R. Beyar, S.Israelit, S. Tzafrir), IBM Research (OCR Project), Hapoalim Bank (G.Maklef, T. Shlasky), Pelephone Cellular, . . .
� Technion SEE Center / Laboratory:Feigin; Trofimov, Nadjharov, Gavako, Kutsy; Liberman, Koren,Plonsky, Senderovic; Research Assistants, . . .
� Empirical/Statistical Analysis:Brown, Gans, Zhao; Shen; Ritov, Goldberg; Gurvich, Huang,Liberman; Armony, Marmor, Tseytlin, Yom-Tov; Zeltyn, Nardi,Gorfine, . . .
2 2
Contents
� Service Systems: Call Centers, Hospitals, Websites, · · ·� Prevalent paradigm of modeling and approximations
� Redefining the role of Asymptotics, via Data
� ServNets: QNets, SimNets; FNets, DNets
� Ultimate Goal: Data-based creation and validationof ServNets, automatically in real-time
3 3
Contents
� Service Systems: Call Centers, Hospitals, Websites, · · ·� Prevalent paradigm of modeling and approximations
� Redefining the role of Asymptotics, via Data
� ServNets: QNets, SimNets; FNets, DNets
� Ultimate Goal: Data-based creation and validationof ServNets, automatically in real-time
� Why be Optimistic? Pilot at the Technion SEELab
3 4
Contents
� Service Systems: Call Centers, Hospitals, Websites, · · ·� Prevalent paradigm of modeling and approximations
� Redefining the role of Asymptotics, via Data
� ServNets: QNets, SimNets; FNets, DNets
� Ultimate Goal: Data-based creation and validationof ServNets, automatically in real-time
� Why be Optimistic? Pilot at the Technion SEELab
� Related themes: Process Mining (BPM), Networks (Social,Biological,· · · ), “Almost-Complex" Systems, Simulation-based. . .,
� Scenic Route: Open Problems, New Directions, UnchartedTerritories
3 5
On Asymptotic Research of Queueing Systems
Queueing asymptotics has grown to become a central researchtheme in Operations Research and Applied Probability, beyond justqueueing theory. Its claim to fame has been the deep insights that itprovides into the dynamics of Queueing Networks (QNets), andrightly so:
� Kingman’s invariance principle in conventional heavy-traffic� Whitt’s sample-path (functional) framework� Reiman’s network analysis via oblique reflection� Bramson-Williams’ framework for state-space collapse� Laws’ resource pooling� Harrison’s paradigm for asymptotic control (Wein; van Mieghem’s Gcμ)� Dai’s fluid-based stability� Halfin-Whitt’s (QED regime) (√-staffing for many-server queues)� P = NP : Atar’s equivalence of Preemptive and Non-Preemptive SBR;
Stolyar, Gurvich� Massey-Whitt’s research of time-varying queues
4 6
On Asymptotic Research of Queueing Systems
Queueing asymptotics has grown to become a central researchtheme in Operations Research and Applied Probability, beyond justqueueing theory. Its claim to fame has been the deep insights that itprovides into the dynamics of Queueing Networks (QNets), andrightly so:
� Kingman’s invariance principle in conventional heavy-traffic� Whitt’s sample-path (functional) framework� Reiman’s network analysis via oblique reflection� Bramson-Williams’ framework for state-space collapse� Laws’ resource pooling� Harrison’s paradigm for asymptotic control (Wein; van Mieghem’s Gcμ)� Dai’s fluid-based stability� Halfin-Whitt’s (QED regime) (√-staffing for many-server queues)� P = NP : Atar’s equivalence of Preemptive and Non-Preemptive SBR;
Stolyar, Gurvich� Massey-Whitt’s research of time-varying queues
4 7
Applying Queueing Asymptotics
Has it helped one approximate or simulate a service systemmore efficiently, estimate its parameters more accurately, teachit to our students more effectively, perhaps even manage thesystem better?
I am of the opinion that the answers to such questions havebeen too often negative, that positive answers must have theoryand applications nurture each other, which is good, and myapproach to make this good happen is by marrying theory with
data .
5 8
Models Approximations
QNets SimNets
Accuracy
Phenomenology
Prevalent Asymptotic Approximations
System (Data)
6 9
Models Approximations
QNets SimNets FNet DNet Models
Accuracy
Phenomenology
X
Data–Based Prevalent Asymptotic Approximations Models
System (Data)
X X
7 10
Models Approximations
QNets SimNets FNet DNet Models
Accuracy
Phenomenology Value
XX
Data–Based Prevalent Asymptotic Approximations Models
System (Data)
X X
8 11
Value
Call-Center Network: Gallery of Models
Agents(CSRs)
Back-Office
Experts)(Consultants
VIP)Training (
Arrivals(Business Frontier
of the21th Century)
Redial(Retrial)
Busy)Rare(
Goodor
Bad
Positive: Repeat BusinessNegative: New Complaint
Lost Calls
Abandonment
Agents
ServiceCompletion
Service Engineering: Multi-Disciplinary Process View
ForecastingStatistics
New Services Design (R&D)Operations,Marketing
Organization Design:Parallel (Flat)Sequential (Hierarchical)Sociology/Psychology,Operations Research
Human Resource Management
Service Process Design
To Avoid Delay
To Avoid Starvation Skill Based Routing
(SBR) DesignMarketing,Human Resources,Operations Research,MIS
CustomersInterface Design
Computer-TelephonyIntegration - CTIMIS/CS
Marketing
Operations/BusinessProcessArchiveDatabaseDesignData Mining:MIS, Statistics, OperationsResearch,Marketing
InternetChatEmailFax
Lost Calls
Service Completion)75% in Banks (
( Waiting TimeReturn Time)
Logistics
CustomersSegmentation -CRM
Psychology, OperationsResearch,Marketing
Expect 3 minWilling 8 minPerceive 15 min
PsychologicalProcessArchive
Psychology,Statistics
Training, IncentivesJob Enrichment
Marketing,Operations Research
Human Factors Engineering
VRU/IVR
Queue)Invisible (
VIP Queue
(If Required 15 min,then Waited 8 min)(If Required 6 min,then Waited 8 min)
Information DesignFunctionScientific DisciplineMulti-Disciplinary
IndexCall Center Design
(Turnover up to 200% per Year)(Sweat Shops
of the21th Century)
Tele-StressPsychology
18 13
Call-Center Network: Gallery of Models
Agents(CSRs)
Back-Office
Experts)(Consultants
VIP)Training (
Arrivals(Business Frontier
of the21th Century)
Redial(Retrial)
Busy)Rare(
Goodor
Bad
Positive: Repeat BusinessNegative: New Complaint
Lost Calls
Abandonment
Agents
ServiceCompletion
Service Engineering: Multi-Disciplinary Process View
ForecastingStatistics
New Services Design (R&D)Operations,Marketing
Organization Design:Parallel (Flat)Sequential (Hierarchical)Sociology/Psychology,Operations Research
Human Resource Management
Service Process Design
To Avoid Delay
To Avoid Starvation Skill Based Routing
(SBR) DesignMarketing,Human Resources,Operations Research,MIS
CustomersInterface Design
Computer-TelephonyIntegration - CTIMIS/CS
Marketing
Operations/BusinessProcessArchiveDatabaseDesignData Mining:MIS, Statistics, OperationsResearch,Marketing
InternetChatEmailFax
Lost Calls
Service Completion)75% in Banks (
( Waiting TimeReturn Time)
Logistics
CustomersSegmentation -CRM
Psychology, OperationsResearch,Marketing
Expect 3 minWilling 8 minPerceive 15 min
PsychologicalProcessArchive
Psychology,Statistics
Training, IncentivesJob Enrichment
Marketing,Operations Research
Human Factors Engineering
VRU/IVR
Queue)Invisible (
VIP Queue
(If Required 15 min,then Waited 8 min)(If Required 6 min,then Waited 8 min)
Information DesignFunctionScientific DisciplineMulti-Disciplinary
IndexCall Center Design
(Turnover up to 200% per Year)(Sweat Shops
of the21th Century)
Tele-StressPsychology
19 14
Retail
PremierBusiness Platinum Consumer Loans Online BankingEBO TelesalesSubanco Case Quality Priority Service AST CCO Quick&Reilly BPS
1_1 1_57 1_15 2_3 2_63_1 3_5 5_1 6 8 10_1 11 12 13 15 17
10430 189932947 384 9840 157
54 1455 25755551 2372 597 91 195 342 3660 2173639 3251325 487 32 12 619 2352 3668 4844 447
The Basic Staffing Model: Erlang-A (M/M/N + M)agents
arrivals
abandonment
1
2
n
…
queue
Erlang-A (Palm 1940’s) = Birth & Death Q, with parameters:
� λ – Arrival rate (Poisson)� μ – Service rate (Exponential; E [S] = 1
μ )
� θ – Patience rate (Exponential, E [Patience] = 1θ )
� N – Number of Servers (Agents).69 17
Erlang-A: Practical Relevance?
Experience:� Arrival process not pure Poisson (time-varying, σ2 too large)� Service times not Exponential (typically close to LogNormal)� Patience times not Exponential (various patterns observed).
70 18
Erlang-A: Practical Relevance?
Experience:� Arrival process not pure Poisson (time-varying, σ2 too large)� Service times not Exponential (typically close to LogNormal)� Patience times not Exponential (various patterns observed).
� Building Blocks need not be independent (eg. long waitassociated with long service; with w/ M. Reich and Y. Ritov)
� Customers and Servers not homogeneous (classes, skills)� Customers return for service (after busy, abandonment;
dependently; P. Khudiakov, M. Gorfine, P. Feigin)� · · · , and more.
70 19
Erlang-A: Practical Relevance?
Experience:� Arrival process not pure Poisson (time-varying, σ2 too large)� Service times not Exponential (typically close to LogNormal)� Patience times not Exponential (various patterns observed).
� Building Blocks need not be independent (eg. long waitassociated with long service; with w/ M. Reich and Y. Ritov)
� Customers and Servers not homogeneous (classes, skills)� Customers return for service (after busy, abandonment;
dependently; P. Khudiakov, M. Gorfine, P. Feigin)� · · · , and more.
Question: Is Erlang-A Relevant?
YES ! Fitting a Simple Model to a Complex Reality, bothTheoretically and Practically
70 20
Erlang-A: Fitting a Simple Model to a Complex Reality
Hourly Performance vs. Erlang-A Predictions (1 year)
% Abandon E[Wait] %{Wait > 0}
0 0.1 0.2 0.3 0.4 0.5 0.60
0.1
0.2
0.3
0.4
0.5
Probability to abandon (Erlang−A)
Pro
babi
lity
to a
band
on (d
ata)
0 50 100 150 200 2500
50
100
150
200
250
Waiting time (Erlang−A), sec
Wai
ting
time
(dat
a), s
ec
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Probability of wait (Erlang−A)
Pro
babi
lity
of w
ait (
data
)
� Empirically-Based & Theoretically-Supported Estimation of(Im)Patience: θ = P{Ab}/E[Wq])
� Small Israeli Bank (more examples in progress)� Hourly performance vs. Erlang-A predictions, 1 year: aggregated
groups of 40 similar hours71 21
Universal Approximations: Erlang-A (M/M/N + M)agents
arrivals
abandonment
1
2
n
…
queuew/ I. Gurvich & J. Huang
82 22
Universal Approximations: Erlang-A (M/M/N + M)agents
arrivals
abandonment
1
2
n
…
queuew/ I. Gurvich & J. Huang
� QNet: Birth & Death Queue, with B - D rates
F (q) = λ− μ · (q ∧ n)− θ · (q − n)+, q = 0, 1, . . .
82 23
F q n q n +F (q) = λ− μ · (q ∧ n)− θ · (q − n)+,
Universal Approximations: Erlang-A (M/M/N + M)agents
arrivals
abandonment
1
2
n
…
queuew/ I. Gurvich & J. Huang
� QNet: Birth & Death Queue, with B - D rates
F (q) = λ− μ · (q ∧ n)− θ · (q − n)+, q = 0, 1, . . .
� FNet: Dynamical (Deterministic) System – ODEdxt = F (xt)dt , t ≥ 0
82 24
dxtxx F xtxx dt ,= F (xt)d
Universal Approximations: Erlang-A (M/M/N + M)agents
arrivals
abandonment
1
2
n
…
queuew/ I. Gurvich & J. Huang
� QNet: Birth & Death Queue, with B - D rates
F (q) = λ− μ · (q ∧ n)− θ · (q − n)+, q = 0, 1, . . .
� FNet: Dynamical (Deterministic) System – ODEdxt = F (xt)dt , t ≥ 0
� DNet: Universal (Stochastic) Approximation – SDE
dYt = F (Yt)dt +√
2λ dBt , t ≥ 0
eg. μ = θ, or n = ∞: x = λ− μ · x , Y = OU process
Accuracy increases as λ ↑ ∞ (no additional assumptions)83 25
,dBt ,
Universal Approximation: Why 2λ?
� Semi-martingale representation of the B&D process:Fluid + Martingale
� Predictable quadratic variation:∫ t
0[λ+ μ(Qs ∧ n) + θ(Qs − n)+]ds
� In steady-state, arrival rate ≡ departure rate:
λ = E[μ(Qs ∧ n) + θ(Qs − n)+]
� Expectation of the predictable quadratic variation:
E
∫ t
0[λ+ μ(Qs ∧ n) + θ(Qs − n)+]ds = 2λt
� dMartingalet ≈√
2λ · dBrowniant
94 27
Why 22λ?
Value of Universal Approximation
� Tractable - closed-form stable expressions� Accurate - more than heavy traffic limits� Robust - all many-server regimes, and beyond, with hardly any
assumptions� Value
� Performance Analysis� Optimization (Staffing)� Inference (w/ G. Pang)� Simulation (w. J. Blanchet)
� Limitation: Steady-State (but working on it)
Why does it work so well?
Coupling “Busy" + “Idle" Excursions of B&D and the correspondingDiffusion (durations order 1√
λ)
83 26
Inference SimLab
Control
Design
Predictions
Models Approximations
QNets SimNets FNet DNet Models
Accuracy
Phenomenology Value
XX
X
Data–Based Prevalent Asymptotic Approximations Models
System (Data)
X X
10 28
System = Coin Tossing, Model = Binomial ; de Moivre 1738
Approx. / Models: SLLN (FNets), CLT (DNets) ; Laplace 1810
Value: Exceeds Value of originating stylized model
Normal, Brownian Motion ; Bachalier 1900
Poisson ; Poisson 1838
Models Approximations
QNets SimNets FNet DNet Models
Accuracy
Phenomenology Value
XX
Data–Based Prevalent Asymptotic Approximations Models
System (Data)
X X
9 29
Normal,
Poisson
Coin Tossing, Binomial
SLLN CLT
Asymptotic Landscape: 9 Operational Regimes, and then someErlang-A, w/ I. Gurvich & J. Huang
Erlang-A Conventional scaling Many-Server scaling NDS scalingμ & θ fixed Sub Critical Over QD QED ED Sub Critical OverOffered load 1
1+δ1− β√
n1
1−γ1
1+δ1− β√
n1
1−γ1
1+δ 1− βn
11−γper server
Arrival rate λ μ1+δ
μ− β√nμ μ
1−γnμ1+δ
nμ− βμ√
n nμ1−γ
nμ1+δ
nμ− βμ nμ1−γ
# servers 1 n nTime-scale n 1 n
Impatience rate θ/n θ θ/n
Staffing level λμ(1 + δ) λ
μ(1 + β√
n) λ
μ(1− γ) λ
μ(1 + δ) λ
μ+ β
√λμ
λμ(1− γ) λ
μ(1 + δ) λ
μ+ β λ
μ(1− γ)
Utilization 11+δ
1−√
θμ
h(β)√n
1 11+δ
1−√
θμ
h(β)√n
1 11+δ
1−√
θμ
h(β)n
1
E(Q) 1δ(1+δ)
√ng(β) nμγ
θ(1−γ)1δ�n
√ng(β)α nμγ
θ(1−γ)o(1) ng(β) n2μγ
θ(1−γ)
P(Ab) 1n
1δ
θμ
θ√nμ
g(β) γ 1n
(1+δ)δ
θμ�n
θ√nμ
g(β)α γ o( 1n2 )
θnμ
g(β) γ
P(Wq > 0) 11+δ
≈ 1 �n α ∈ (0,1) ≈ 1 ≈ 0 ≈ 1
P(Wq > T ) 11+δ
e− δ
1+δμT 1 +O( 1√
n) 1 +O( 1
n) ≈ 0 f(T ) ≈ 0 Φ(β+
√θμT )
Φ(β)1 +O( 1
n)
CongestionEWq
ES1δ
√ng(β) nμγ/θ 1
n(1+δ)
δ�n
α√ng(β) μγ
θo( 1
n) g(β) nμγ/θ
� Conventional: Ward & Glynn (03, G/G/1 + G)� Many-Server:
� QED: Halfin-Whitt (81), Garnett-M-Reiman (02)� ED: Whitt (04)� NDS: Atar (12)
81 30
Conventional Many--Server- NDSQEDQEDQDQD EDED
Offered load
# servers
Staffing
Asymptotic Landscape: 9 Operational Regimes, and then someErlang-A, w/ I. Gurvich & J. Huang
Erlang-A Conventional scaling Many-Server scaling NDS scalingμ & θ fixed Sub Critical Over QD QED ED Sub Critical OverOffered load 1
1+δ1− β√
n1
1−γ1
1+δ1− β√
n1
1−γ1
1+δ 1− βn
11−γper server
Arrival rate λ μ1+δ
μ− β√nμ μ
1−γnμ1+δ
nμ− βμ√
n nμ1−γ
nμ1+δ
nμ− βμ nμ1−γ
# servers 1 n nTime-scale n 1 n
Impatience rate θ/n θ θ/n
Staffing level λμ(1 + δ) λ
μ(1 + β√
n) λ
μ(1− γ) λ
μ(1 + δ) λ
μ+ β
√λμ
λμ(1− γ) λ
μ(1 + δ) λ
μ+ β λ
μ(1− γ)
Utilization 11+δ
1−√
θμ
h(β)√n
1 11+δ
1−√
θμ
h(β)√n
1 11+δ
1−√
θμ
h(β)n
1
E(Q) 1δ(1+δ)
√ng(β) nμγ
θ(1−γ)1δ�n
√ng(β)α nμγ
θ(1−γ)o(1) ng(β) n2μγ
θ(1−γ)
P(Ab) 1n
1δ
θμ
θ√nμ
g(β) γ 1n
(1+δ)δ
θμ�n
θ√nμ
g(β)α γ o( 1n2 )
θnμ
g(β) γ
P(Wq > 0) 11+δ
≈ 1 �n α ∈ (0,1) ≈ 1 ≈ 0 ≈ 1
P(Wq > T ) 11+δ
e− δ
1+δμT 1 +O( 1√
n) 1 +O( 1
n) ≈ 0 f(T ) ≈ 0 Φ(β+
√θμT )
Φ(β)1 +O( 1
n)
CongestionEWq
ES1δ
√ng(β) nμγ/θ 1
n(1+δ)
δ�n
α√ng(β) μγ
θo( 1
n) g(β) nμγ/θ
� Conventional: Ward & Glynn (03, G/G/1 + G)� Many-Server:
� QED: Halfin-Whitt (81), Garnett-M-Reiman (02)� ED: Whitt (04)� NDS: Atar (12)
� “Missing": ED+QED; Hazard-rate scaling (M/M/N+G); Time-Varying,Non-Parametric; Moderate- and Large-Deviation; Networks; Control
81 31
“Missing":
Protocols: Staffing (N) vs. Offered-Load (R = λ× E(S))IL Telecom; June-September, 2004; w/ Nardi, Plonski, Zeltyn
2205 half-hour intervals (13 summer weeks, week-days)67 32
Operation Focus: The “Production of Justice"The Labor-Court Process in Haifa, Israel
Queue
Mile Stone
Activity
Appeal
Proceedings
Closure
PrepareAllocateOpen File
Avg. sojourn time in months / years
Processing time in mins / hours / days
Phase Transition
Phase
• Operational Performance surrogate for
Financial, Psychological, Clinical,. . .14 36
Call Centers, Then Hospitals, Now Internet
Call Centers - U.S. Stat.
� $200 – $300 billion annual expenditures� 100,000 – 200,000 call centers� “Window" into the company, for better or worse� Over 3 million agents = 2% – 4% workforce
15 37
Call Centers, Then Hospitals, Now Internet
Call Centers - U.S. Stat.
� $200 – $300 billion annual expenditures� 100,000 – 200,000 call centers� “Window" into the company, for better or worse� Over 3 million agents = 2% – 4% workforce
Healthcare - similar and unique challenges:
� Cost-figures far more staggering� Risks much higher� ED (initial focus) = hospital-window� Over 3 million nurses
Internet - . . .
15 39
Emergency-Department Network: Gallery of Models
ImagingLaboratory
Experts
Interns
Returns (Old or New Problem)
“Lost” Patients
LWBS
Nurses
Statistics,HumanResourceManagement(HRM)
New Services Design (R&D)Operations,Marketing,MIS
Organization Design:Parallel (Flat) = ERvs. a true ED Sociology, Psychology,Operations Research
Service Process Design
Quality
Efficiency
CustomersInterface Design
Medicine
(High turnoversMedical-Staff shortage)
Operations/BusinessProcessArchiveDatabaseDesignData Mining:MIS, Statistics, OperationsResearch,Marketing
StretcherWalking
Service Completion(sent to other department)
( Waiting TimeActive Dashboard )
PatientsSegmentation
Medicine,Psychology, Marketing
PsychologicalProcessArchive
Human FactorsEngineering(HFE)
InternalQueue
OrthopedicQueue
Arrivals
FunctionScientific DisciplineMulti-Disciplinary
Index
ED-StressPsychology
OperationsResearch, Medicine
Emergency-Department Network: Gallery of Models
Returns
TriageReception
Skill Based Routing (SBR) DesignOperations Research,HRM, MIS, Medicine
IncentivesGame Theory,Economics
Job EnrichmentTrainingHRM
HospitalPhysiciansSurgical
Queue
Acute,Walking
Blocked(Ambulance Diversion)
Forecasting
Information DesignMIS, HFE,Operations Research
Psychology,Statistics
Home
� Forecasting, Abandonment = LWBS, SBR ≈ Flow Control24 41
Prerequisite I: Data
Averages Prevalent (and could be useful / interesting).But I need data at the level of the Individual Transaction:For each service transaction (during a phone-service in a call center,or a patient’s visit in a hospital, or browsing in a website, or . . .), itsoperational history = time-stamps of events (events-log files).
25 43
Beyond Averages: The Human Factor
Histogram of Service-Time in an Israeli Call Center, 1999
January-OctoberJanuary-October
0
2
4
6
8
0 100 200 300 400 500 600 700 800 900
AVG: 185STD: 238
?6.83%
November-DecemberNovember-December
0
2
4
6
8
0 100 200 300 400 500 600 700 800 900
AVG: 201STD: 263
5.59%
Log-Normal
� 6.8% Short-Services:
26 44
Human
Beyond Averages: The Human Factor
Histogram of Service-Time in an Israeli Call Center, 1999
January-OctoberJanuary-October
0
2
4
6
8
0 100 200 300 400 500 600 700 800 900
AVG: 185STD: 238
?6.83%
November-DecemberNovember-December
0
2
4
6
8
0 100 200 300 400 500 600 700 800 900
AVG: 201STD: 263
5.59%
Log-Normal
� 6.8% Short-Services: Agents’ “Abandon" (improve bonus, rest),(mis)lead by incentives
� Distributions must be measured (in seconds = natural scale)� LogNormal service times common in call centers
26 45
Durations: Phone Calls (2 Surprises)
Israeli Call Center, Nov–Dec, 1999
Log(Service Times)
0 2 4 6 8
0.0
0.1
0.2
0.3
0.4
Log(Service Time)
Pro
porti
on
LogNormal QQPlot
Log-normal
Ser
vice
tim
e
0 1000 2000 30000
1000
2000
3000
� Practically Important: (mean, std)(log) characterization� Theoretically Intriguing: Why LogNormal ? Naturally multiplicative
but, in fact, also Infinitely-Divisible (Generalized Gamma-Convolutions)
54 46
Infinitely--Divisible-
Technion SEE = Service Enterprise Engineering
SEELab: Data-repositories for research and teaching
� For example:� Bank Anonymous: 1 years, 350K calls by 15 agents - in 2000.
Brown, Gans, Sakov, Shen, Zeltyn, Zhao (JASA), paved the wayfor:
� U.S. Bank: 2.5 years, 220M calls, 40M by 1000 agents.� Israeli Cellular: 2.5 years, 110M calls, 25M calls by 750 agents.� Israeli Bank: from January 2010, daily-deposit at a SEESafe.� Israeli Hospital: 4 years, 1000 beds; 8 ED’s- Sinreich’s data.
29 49
Technion SEE = Service Enterprise Engineering
SEELab: Data-repositories for research and teaching
� For example:� Bank Anonymous: 1 years, 350K calls by 15 agents - in 2000.
Brown, Gans, Sakov, Shen, Zeltyn, Zhao (JASA), paved the wayfor:
� U.S. Bank: 2.5 years, 220M calls, 40M by 1000 agents.� Israeli Cellular: 2.5 years, 110M calls, 25M calls by 750 agents.� Israeli Bank: from January 2010, daily-deposit at a SEESafe.� Israeli Hospital: 4 years, 1000 beds; 8 ED’s- Sinreich’s data.
SEEStat: Environment for graphical EDA in real-time
� Universal Design, Internet Access, Real-Time Response.
SEEServer: Free for academic useRegister; access U.S. Bank, Israeli Bank, Rambam Hospital.
29 50
eg. RFID-Based Data: Mass Casualty Event (MCE)Drill: Chemical MCE, Rambam Hospital, May 2010
Focus on severely wounded casualties (≈ 40 in drill)Note: 20 observers support real-time control (helps validation)
30 51
Data Cleaning: MCE with RFID SupportData-base Company report comment
Asset id order Entry date Exit date Entry date Exit date 4 1 1:14:07 PM 1:14:00 PM 6 1 12:02:02 PM 12:33:10 PM 12:02:00 PM 12:33:00 PM 8 1 11:37:15 AM 12:40:17 PM 11:37:00 AM exit is missing
10 1 12:23:32 PM 12:38:23 PM 12:23:00 PM 12 1 12:12:47 PM 12:35:33 PM 12:35:00 PM entry is missing 15 1 1:07:15 PM 1:07:00 PM 16 1 11:18:19 AM 11:31:04 AM 11:18:00 AM 11:31:00 AM 17 1 1:03:31 PM 1:03:00 PM 18 1 1:07:54 PM 1:07:00 PM 19 1 12:01:58 PM 12:01:00 PM 20 1 11:37:21 AM 12:57:02 PM 11:37:00 AM 12:57:00 PM 21 1 12:01:16 PM 12:37:16 PM 12:01:00 PM
22 1 12:04:31 PM 12:20:40 PMfirst customer is missing
22 2 12:27:37 PM 12:27:00 PM 25 1 12:27:35 PM 1:07:28 PM 12:27:00 PM 1:07:00 PM 27 1 12:06:53 PM 12:06:00 PM
28 1 11:21:34 AM 11:41:06 AM 11:41:00 AM 11:53:00 AMexit time instead of entry time
29 1 12:21:06 PM 12:54:29 PM 12:21:00 PM 12:54:00 PM 31 1 11:40:54 AM 12:30:16 PM 11:40:00 AM 12:30:00 PM 31 2 12:37:57 PM 12:54:51 PM 12:37:00 PM 12:54:00 PM 32 1 11:27:11 AM 12:15:17 PM 11:27:00 AM 12:15:00 PM 33 1 12:05:50 PM 12:13:12 PM 12:05:00 PM 12:15:00 PM wrong exit time 35 1 11:31:48 AM 11:40:50 AM 11:31:00 AM 11:40:00 AM 36 1 12:06:23 PM 12:29:30 PM 12:06:00 PM 12:29:00 PM 37 1 11:31:50 AM 11:48:18 AM 11:31:00 AM 11:48:00 AM 37 2 12:59:21 PM 12:59:00 PM
- Imagine “Cleaning" 60,000+ customers per day (call centers) !
- “Psychology" of Data Trust and Transfer (e.g. 2 years till transfer)31 52
The Basic Service-Network Model: Erlang-R
w/ G. Yom-Tov Needy (st-servers)
rate-
Content (Delay) rate -
1-p
p
1
2
Arrivals Poiss( t) Patient discharge
Erlang-R (IE: Repairman Problem 50’s; CS: Central-Server 60’s) =2-station “Jackson" Network = (M/M/S, M/M/∞) :
� λt – Time-Varying Arrival rate� St – Number of Servers (Nurses / Physicians).� μ – Service rate (E [Service] = 1
μ)
� p – ReEntrant (Feedback) fraction� δ – Content-to-Needy rate (E [Content] = 1
δ)
63 53
Erlang-R: Fitting a Simple Model to a Complex Reality
Chemical MCE Drill (Israel, May 2010)
Arrivals & Departures (RFID) Erlang-R (Fluid, Diffusion)
0
10
20
30
40
50
60
11:02 11:16 11:31 11:45 12:00 12:14 12:28 12:43 12:57 13:12 13:26
Tota
l Nu
mb
er
of
Pat
ien
ts
Time
Cumulative Arrivals
Cumulative Departures
15
20
25
30
erof
MCE
Patien
tsinED
Actual Q(t)
Fluid Q(t)
Lower Envelope Q(t) (Theoretical)
Upper Envelope Q(t) (Theoretical)
Fluid Q1
0
5
10
11:02 11:16 11:31 11:45 12:00 12:14 12:28 12:43 12:57 13:12 13:26
Num
beTime
� Recurrent/Repeated services in MCE Events: eg. Injection every 15 minutes
65 56
Erlang-R: Fitting a Simple Model to a Complex Reality
Chemical MCE Drill (Israel, May 2010)
Arrivals & Departures (RFID) Erlang-R (Fluid, Diffusion)
0
10
20
30
40
50
60
11:02 11:16 11:31 11:45 12:00 12:14 12:28 12:43 12:57 13:12 13:26
Tota
l Nu
mb
er
of
Pat
ien
ts
Time
Cumulative Arrivals
Cumulative Departures
15
20
25
30
erof
MCE
Patien
tsinED
Actual Q(t)
Fluid Q(t)
Lower Envelope Q(t) (Theoretical)
Upper Envelope Q(t) (Theoretical)
Fluid Q1
0
5
10
11:02 11:16 11:31 11:45 12:00 12:14 12:28 12:43 12:57 13:12 13:26
Num
beTime
� Recurrent/Repeated services in MCE Events: eg. Injection every 15 minutes� Fluid (Sample-path) Modeling, via Functional Strong Laws of Large Numbers� Stochastic Modeling, via Functional Central Limit Theorems
� ED in MCE: Confidence-interval, usefully narrow for Control� ED in normal (time-varying) conditions: Personnel Staffing65 57
The Asymptotic Framework: Erlang-R in the ED
System = Emergency Department (eg. Rambam Hospital)� SimNet = Customized ED-Simulator (Marmor & Sinreich)� QNet = Erlang-R (time-varying 2-station Jackson; w/ Yom-Tov)� FNet = 2-dim dynamical system (Massey & Whitt)� DNet = 2-dim Markovian Service Net (w/ Massey and Reiman)
66 58
The Asymptotic Framework: Erlang-R in the ED
System = Emergency Department (eg. Rambam Hospital)� SimNet = Customized ED-Simulator (Marmor & Sinreich)� QNet = Erlang-R (time-varying 2-station Jackson; w/ Yom-Tov)� FNet = 2-dim dynamical system (Massey & Whitt)� DNet = 2-dim Markovian Service Net (w/ Massey and Reiman)
Asymptotic Framework� Start with Data� Fit a simple QNet (time-varying Erlang-R)
to a complex reality (ED Physicians)� Develop FNet (Offered-Load of Physicians) and DNet� Use QNet + FNet + DNet for Design (√-Staffing), Analysis (of
Feedback), . . .� Virtual reality: SimNet of ED with √-staffing of Physicians)� Validation: stable performance, confidence intervals, . . .
66 59
ServNets: Data-Based Online Automatic Creationw/ V. Trofimov, E. Nadjharov, I. Gavako = Technion SEELab
� Towards creating ServNets = QNets, SimNets, FNets, DNets
� SimNets of Service Systems = Virtual Realities, for ExploratoryData Analysis (EDA), Performance Analysis, Optimization, . . .
� SimNets also of QNEts, FNets, DNets, for “Valuation"(Validation, Accuracy)
32 60
ServNets: Data-Based Online Automatic Creationw/ V. Trofimov, E. Nadjharov, I. Gavako = Technion SEELab
� Towards creating ServNets = QNets, SimNets, FNets, DNets
� SimNets of Service Systems = Virtual Realities, for ExploratoryData Analysis (EDA), Performance Analysis, Optimization, . . .
� SimNets also of QNEts, FNets, DNets, for “Valuation"(Validation, Accuracy)
� Ultimately: Empirical Research Lab, necessitated by thecomplexity of service systems and human-behavior:
� Daily routine in Physics, Chemistry, Biology; Psychology� But also in Transportation (Science), and recently (Behavioral)
Economics
� Why not in Service Science / Engineering / Management ?
32 61
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Entry
VRURetail
VRUPremier
VRUBusiness
VRUConsumer Loans
VRUSubanco
VRUSummit
Business LineRetail
Business LinePremier
Business LineBusiness
Business LinePlatinum
Business LineConsumer Loans
Business LineOnline Banking
Business LineEBO
Business LineTelesales
Business LineSubanco
Business LineSummit
AnnouncementRetail
AnnouncementPremier
AnnouncementPlatinum
AnnouncementConsumer Loans
AnnouncementOnline Banking
AnnouncementTelesales
AnnouncementSubanco
MessageRetail
MessagePremier
MessageBusiness
MessagePlatinum
MessageConsumer Loans
MessageTelesales
NonBusiness LineBusiness
NonBusiness LineSubanco
NonBusiness LinePriority Service
NonBusiness Line NonCC ServiceCCO
NonCC ServiceQuick&Reilly
Overnight ClosedRetail
Overnight ClosedConsumer Loans
Overnight ClosedEBO
TrunkRetail
TrunkPremier
TrunkBusiness
TrunkConsumer Loans
TrunkOnline Banking
TrunkEBO
TrunkTelesales
TrunkPriority Service
Trunk
Trunk
Trunk
Trunk
Trunk
InternalTotal
OutgoingTotal
NormalTermination
NormalTermination
UndeterminedTermination
AbandonedShort
Abandoned
OtherUnhandled
Transfer
Transfer
1 Day in a Call Center - Customers
USBank April 2, 2001
62
33975
4221
2006
2886
2741
361
354697
1111
43
1049
994
319
162
2281
3908
160
504
266
193
122
158
118
7
1
32246
35916
1259
2006
2823
3798
876 352
370
107 491
545
566
127
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Entry
VRURetail
VRUPremier
VRUBusiness
VRUConsumer Loans
VRUSubanco
VRUSummit
Business LineRetail
Business LinePremier
Business LineBusiness
Business LinePlatinum
Business LineConsumer Loans
Business LineOnline Banking
Business LineEBO
Business LineTelesales
Business LineSubanco
Business LineSummit
AnnouncementRetail
AnnouncementPremier
AnnouncementPlatinum
AnnouncementConsumer Loans
AnnouncementOnline Banking
AnnouncementTelesales
AnnouncementSubanco
MessageRetail
MessagePremier
MessageBusiness
MessagePlatinum
MessageConsumer Loans
MessageTelesales
NonBusiness LineBusiness
NonBusiness LineSubanco
NonBusiness LinePriority Service
NonBusiness Line NonCC ServiceCCO
NonCC ServiceQuick&Reilly
Overnight ClosedRetail
Overnight ClosedConsumer Loans
Overnight ClosedEBO
TrunkRetail
TrunkPremier
TrunkBusiness
TrunkConsumer Loans
TrunkOnline Banking
TrunkEBO
TrunkTelesales
TrunkPriority Service
Trunk
Trunk
Trunk
Trunk
Trunk
InternalTotal
OutgoingTotal
NormalTermination
NormalTermination
UndeterminedTermination
AbandonedShort
Abandoned
OtherUnhandled
Transfer
Transfer
1 Day in a Call Center - Customers
USBank April 2, 2001
63
ED
Pediatric
Neurology Nephrology Derrmatology
Internal
IntensiveCare
Cardiology
Rheumatology
UrologyOtorhinolaryngology Orthopedics
Surgery
Maternity
Gynecology
Psychiatry Ophthalmology
R
L
D
Out
R
R
R
R
R R
R
RR RR
R
R
R
R
R
L
LL
L
L
L
L
L
L
D
D
D
D
D DD
D
DD
D
D
Out
Out
Out
Out Out
Out
OutOut Out OutOut
Out
Out
1 Day in a Hospital - Patients
Rambam August, 2004
Released (Home)
Left with Medical File
Deceased
Transfer
66
Hospital
115
17
5
43
2
1
1
1
8
6
2
1
1
2
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1
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serveng
lectures
references
predictionmay1809.pdf
homeworks
hw1_amusement_park_mgt.pdf
recitations
hazard_phase_type.pdf
course2011winter
icpr_service_engineering.pdfon_cc_data_frommsom.pdf pivot_table.pdf
thesis_polyna.pdf
proposal_polina.pdf
moss.pdf
files
nurse_proj_psu_tech.pdf
national_cranberry_1.pdf
hw9par_sol_2012w.pdf
syllabus8.pdfexams
statanalysis.pdf
agent-heterogeneity-brown-book-final.pdf
1_1_qed_lecture_introduction_2011w.pdf
course2004
retail.pdf hall_6.pdf
jasa_callcenter.pdf dantzig.pdf
bacceli.pdf
avishai-class-april-2003.ppt
hw7_2011w_par_sol_part2.pdf
ibmrambam technion srii presentation final.ppt
dimensioning.pdf
palmannoyance.pdf
yair_sergurywaitingtimeanalysis.pdf
nejmsb1002320.pdf
qed_qs_scientific_generic_caschina.pdf
web_summary13_2011s.pdf
4callcenters_coverpage.pdf
documentation.pdf rec9part2.pdf
web_summary9_2010w.pdf
qed_qs_scientific_wharton_stat_seminar.pdf
l2_measurements_class_2009s.pdf
ccreview.pdfvdesign_ecompanion.pdf
wharton_lecture_avi_printout.pdflarson_atoa.pdf
proposal_michael.pdf
stanford_seminar_avi_printout.pdf
solver_guide.pdf
fitz.pdf
rec10_part2.pdf rec5.pdf
paxson.pdf
connect_to_see_terminal.pdf
project_ug_simulationinterface.pdf revenue_manage.pdf
hw7_2009s_forecast.xls
syllabus2.pdf
infocom04.pdf
hall_transportation.pdf
whitt_handout_chapter1.pdf
fromprojecttoprocess.pdf
nytimes.2007-06-23.pdf ds_pert_lec1.pdf syllabus6.pdf hw9_2011w.pdf hw7_2011w.pdf
mmng_constraint_supp_or.pdf
awam-april_2011.pdfwhitt_scaling_slides.pdfmmng_seminar.pdf
syllabus4.pdf
syllabus12_2012w.pdf
syllabus5.pdf
mm1_strong_apprximations.pdf seestat_tutorial.ppt
kaplan_porter_2011-9_how-to-solve-the-cost-crisis-in-health-care_hbr.pdf
rec9_part2.pdf
callcenterdata
bocaraton.ps
gccreport 20-04-07 uk version.pdf hall_manpower_planning.pdf
bi18.pdf
syllabus12.pdf fluidview_2010w_short_version.pdf hw7_2009s_par_sol_part2.pdf
moed_b_2007w_solution.pdf
newell.pdf
rec11.pdf
moedb_2009w.pdf
rec3.pdf
hw10_par_sol_2011s.pdf
thirdlevel support ijtm1_cs.pdf
hw4_full.pdf
moedb_2010s_sol.pdf
chandra.pdf
gurvich_seminar.pdf
ed_sinreich_marmor.ppt regimes_supplement.pdf
web_summary10_2011s.pdf hw6par_sol_2009s.xls
exam_2005s_sol.pdf
servicefull.pdf
witor09_empirical_adventures_sep2009.pdf
web_summary12_2011s.pdf
heb_summary_yulia.pdf
hw9par_sol_2011s.pdf
seminar_yulia_9_2.pdf
bpr_2003.pdf staffing_italian_us_2011w.xlsdesignofqueues.pdf thepsychologyofwaitinglines.pdf
erlangabc.pdf
studentsevaluations.pdf hw8_2011s.pdf
hw9_2012w.pdf
edie.pdf
syllabus9.pdf
ds_pert_lec2.pdf
zohar_seminar.ppt
hist-normal.pdf
vandergraft.pdf
rec13.pdf
desighn_ivr.pdf
cohen_aircraft_failures.pdf
sbr.pdf
nano.pdf
hw2_2011w.pdfseminar_presentation_boaz_estimating
er load.ppt
project_ug_meirav.pdf see_report_output_june_2011.pdf
see_report_2010.pdf
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serveng
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hall_flows_hospitals_chapter1text.pdf
references
4callcenterscourse2004 homeworks
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revenue_manage.pdfhw1_amusement_park_mgt.pdf
recitations
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garnett.pdf abandon02.pdf erlang_a.pdf ccbib.pdf
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jasa_callcenter.pdfsbr.pdf
hazard_phase_type.pdf
mazeget_noa_yul.pptexams technion-call-center-report-sept-2004.pdfbrandt.pdf statanalysis.pdfmjp_into_erlang_a.pdf loch.pdf sbr_stolyar.pdf
callcenterdata
larson_atoa.pdf sivanthesisfinal.pdf columbia05.pdf crmis.pptfluid_systems.rar
januarytxt.zip
sbr_wharton_ccforum_short_may03.pdf predictingwaitingtime.pdf avishaicourse_munichor.ppt vdesign_pub.pdf hierarchical_modelling_chen_mandelbaum_part1.pdf
solver_guide.pdf
datamocca_february_2008_cc_forum_lecture.ppt seminar_presentation_galit.pptntro_to_serveng_teaching_note.pdf
pivot_table.pdf
project_ug_simulationinterface.pdf
course2010winter
ed_simulation_modeling_supp.pdf avim_cv.pdfdantzig.pdf yariv_phd.pdf
rec10_part2.pdf
fr6.pdfnejmsb1002320.pdf
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Entry
Entry Entry Entry Entry EntryEntry Entry
VRU
Retail Premier Business PlatinumConsumer Loans EBOTelesales Subanco Summit
VRU
Retail PremierBusiness PlatinumConsumer LoansEBO Telesales SummitOut
VRU
Retail
C
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C
CC C
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1 Hour in a Call Center - Customers - Hierarchical
USBank April 2, 2001
Abandoned Continued (Branch, Another ID)
Completed
70
Hour
Philadelphia NYC
Boston
C C
AA
C
A
USBank April 2, 2001
Zoom Out: Call Center Network Inter-Queues
71
Out: Zoom
Daily(Deposit)
OrderCheckbooks
Identification
ChangePassword
Agent
Fax
Query Transfer
Securities
StockMarket
PerformOperation
Credit
Error
43123
234
270
1352
35315
3900
7895
830
68
65
273
1063
231
768
133
1032
897
40
49
54
21
71
30
165
53
114
29
16
35
10
9
12
107
6
5
21
8
26091
4115
12317
962
1039
147
42
18
28
114
14
72
20
Zoom In: Interactive Voice Response (IVR)
ILBank May 2, 2008
72
In:
ILDUBank January 24, 2010 Agent #043 Shift: 16:00 - 23:45
Inbound Call-Backs
Outgoing
Available Idle
Private Call
Break
73
Private Prepaid
PrivatePrivate VIP Private Customer RetentionBusiness Business VIP Business Customer Retention
Language 2 Prepaid Language 2 Prepaid Low PriorityLanguage 2 PrivateLanguage 3 Internet Surfing Internet
Overseas
1 24 5 810 11 12 1315161718 20 21 24 25
2104
2208 26264592 445 3411432049 1484 8734785 4658 411 444480 43 847 181 974
1253823 843343 1390109630 4454 1240792 3793 49 735
1433 193
Zoom In: Skills - Based Routing (SBR) Network Structure (Protocol)
Israeli Telecom February 10, 2008
N -Design
L -Design
Agent Pool
Customer Class
Connected Component 74
1 24 5 810 11 12 1315161718 20 21 24 25
2104
2208 26264592 445 3411432049 1484 8734785 4658 411 444480 43 847 181 974
1253823 843343 1390109630 4454 1240792 3793 49 735
1433 193
Goal: Data-Based Real-Time Simulation (SimNet)
Private Prepaid Language 3 Language 2 Private Language 2 Prepaid Language 2 Prepaid Low Priority Internet Surfing Internet
Private VIP Private Business Business VIP Business Customer Retention Private Customer Retention Overseas
What is lacking?
1. Dynamics
2. Durations
3. Protocols
Israeli Telecom February 10, 2008
75
Dynamics
Durations
Protocols
Goal:
Dynamics: Time-Varying Arrival-Rates2 Daily Peaks
CC: Dec. 1995, (USA, 700 Helpdesks) CC: May 1959 (England)
Dec 1995!
(Help Desk Institute)
Time24 hrs
% Arrivals
May 1959!
ArrivalRate
Time24 hrs
CC: Nov. 1999 (Israel) ED: Jan.–July 2007 (Israel)Daily
0.00
2.50
5.00
7.50
10.00
12.50
15.00
17.50
20.00
22.50
25.00
27.50
30.00
0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00
Ave
rage
num
ber
of c
ases
Time (Resolution 60 min.)
HomeHospital Patients Arrivals to Emergency Department Total for January2007 February2007 March2007 April2007 May2007 June2007 July2007,Sundays
53 81
1995, 1959
1999 ED: 2007
Durations: Answering MachineIsraeli Bank: IVR/VRU Only, May 2008
IVR_onlyMay 2008, Week days
0.000.100.200.300.400.500.600.700.800.901.001.101.201.301.40
00:00 00:30 01:00 01:30 02:00 02:30 03:00 03:30 04:00 04:30
Time(mm:ss) (Resolution 1 sec.)
Rel
ativ
e fr
eque
ncie
s %
mean=99st.dev.=101
Mixture: 7 LogNormals
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
00:00 00:30 01:00 01:30 02:00 02:30 03:00 03:30 04:00 04:30
Rel
ativ
e fr
eque
ncie
s %
Time(mm:ss) (Resolution 1 sec.)
Fitting Mixtures of Distributions for VRU only timeMay 2008, Week days
Time(mm:ss) (Resolution 1 sec.)Empirical Total Lognormal Lognormal Lognormal
55 82
Mixture:
Durations: Waiting Times in a Call Center⇒ Protocols
Exponential in Heavy-Traffic (min.)Small Israeli Bank
0.00
2.50
5.00
7.50
10.00
12.50
15.00
17.50
20.00
22.50
25.00
27.50
30.00
0.00 100.00 200.00 300.00 400.00 500.00 600.00
Rel
ativ
e fre
quen
cies
%
Time(seconds)( resolution 30)
AnonymousBank Handled Wait Time, TOTAL Total for January1999 February1999 March1999 April1999 May1999 June1999 July1999 August1999 September1999 October1999
November1999 December1999,Weekdays
Empirical Exponential (scale=106.67)
Mean = 106 SD = 109
Routing via Thresholds (sec.)Large U.S. Bank
0.00
2.50
5.00
7.50
10.00
12.50
15.00
17.50
20.00
2.00 7.00 12.00 17.00 22.00 27.00 32.00 37.00
Rel
ativ
e fre
quen
cies
%
Time(seconds)( resolution 1)
USBank Wait time(waiting), Retail May 2002, Weekdays
Scheduling Priorities (sec.) [compare Hospital LOS (hours)]Medium Israeli Bank
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
0.500
0.550
0.600
0.650
20.00 70.00 120.00 170.00 220.00 270.00 320.00 370.00
Rel
ativ
e fre
quen
cies
%
Time(seconds)( resolution 1)
ILBank Wait time (all) August 2007, Weekdays
56 83
LogNormal & Beyond: Length-of-Stay in a Hospital
Israeli Hospital, in Days: LN
0 2 4 6 8 10 13 16 19 22 25 28 31 34 37 40 43 46 49
57 84
Hospital
Days:
LogNormal & Beyond: Length-of-Stay in a Hospital
Israeli Hospital, in Days: LN
0 2 4 6 8 10 13 16 19 22 25 28 31 34 37 40 43 46 49
Israeli Hospital, in Hours: Mixture
0 .2.4 .6 .8 11.21.51.82.12.42.7 33.23.53.84.14.44.7 55.25.55.86.16.46.7 7 7.37.67.98.28.58.89.19.49.710
Explanation: Patients releasedaround 3pm (1pm in Singapore)
Why Bother ?� Hourly Scale: Staffing,. . .� Daily: Flow / Bed Control,. . .
57 85
Hours:
Durations: (Im)Patience while Waiting (Psychology)Palm: (1943–53): Irritation ∝ Hazard Rate
Regular over VIP Customers – Israeli Bank
� Challenges: Un-Censoring, Dependence, Smoothing- requires Call-by-Call Data
58 86
Durations: (Im)Patience while Waiting (Psychology)Palm: (1943–53): Irritation ∝ Hazard Rate
Regular over VIP Customers – Israeli Bank
� Challenges: Un-Censoring, Dependence, Smoothing- requires Call-by-Call Data
� VIP Customers are more Patient (Needy)� Peaks of abandonment at times of Announcements
58 87
Protocols + PsychologyPatient Customers, Announcements, Priority Upgrades
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0 60 120 180 240 300 360 420 480 540 600 660 720 780 840 900
Ha
zard
Fu
nct
ion
Time (seconds)
USBank December 2002, Week days, Quick&Reilly
time willing to wait (hazard rate)
time willing to wait (Pspline)
virtual wait (hazard rate)
virtual wait (Pspline)
59 88
Little’s Law: Call Center & Emergency Department
Time-Gap: # in System lags behind Piecewise-Little (L = λ × W )
USBank Customers in queue(average), Telesales10.10.2001
0.0020.0040.0060.0080.00
100.00120.00140.00160.00180.00200.00
07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00
Time (Resolution 30 min.)
Num
ber o
f cas
es
Customers in queue(average) Little's law
HomeHospital Average patients in EDFebruary 2004, Wednesdays
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00
Time (Resolution 30 min.)
Ave
rage
num
ber o
f cas
es
Average patients in ED Lambda*E(S) smoothed
⇒ Time-Varying Little’s Law� Berstemas & Mourtzinou;� Fralix, Riano, Serfozo; . . .
60 89
ED
Telesales
Congestion Laws: Parsimonious Models3 Queue-Lengths at 30 sec. resolution (ILBank, 10/6/2007)
ILBank Customers in queue (average)10.06.2007
0.00
25.00
50.00
75.00
100.00
125.00
150.00
175.00
200.00
225.00
06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00
Time (Resolution 30 sec.)
Num
ber o
f cas
es
Medium priority Low priority Unidentified
Queue “Shape"ILBank Customers in queue (average)
10.06.2007
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00
Time (Resolution 30 sec.)
Perc
enta
ge
Medium priority Low priority Unidentified
� Area normalized to 100%� State-Space Collapse
61 90
30
Protocols: Staffing (N) vs. Offered-Load (R = λ× E(S))IL Telecom; June-September, 2004; w/ Nardi, Plonski, Zeltyn
2205 half-hour intervals (13 summer weeks, week-days)67 91
The Basic Staffing Model: Erlang-A (M/M/N + M)agents
arrivals
abandonment
1
2
n
…
queue
Erlang-A (Palm 1940’s) = Birth & Death Q, with parameters:
� λ – Arrival rate (Poisson)� μ – Service rate (Exponential; E [S] = 1
μ )
� θ – Patience rate (Exponential, E [Patience] = 1θ )
� N – Number of Servers (Agents).69 92
QED Theory (Erlang ’13; Halfin & Whitt ’81; w/Garnett & Reiman ’02)
Consider a sequence of steady-state M/M/N + M queues, N = 1, 2, 3, . . .Then the following points of view are equivalent, as N ↑ ∞:
• QED %{Cust Wait > 0} ≈ α, 0 < α < 1;
or %{Serv Idle > 0} ≈ 1 − α
• Customers {Abandon} ≈ γ√N, 0 < γ;
• Agents OCC ≈ 1 − β+γ√N
−∞ < β < ∞ ;
• Managers N ≈ R + β√
R , R = λ× E(S) not small;
Here R = Offered Loadeg. R = 25 call/min. × 4 min./call = 100
72 93
Erlang-A: QED Approximations (Examples)
Assume Offered Load R not small (λ → ∞).
Let β = β
√μ
θ, h(·) = φ(·)
1 − Φ(·) = hazard rate of N (0, 1).
� Delay Probability:
P{Wq > 0} ≈[
1 +
√θ
μ· h(β)
h(−β)
]−1
.
� Probability to Abandon:
P{Ab|Wq > 0} ≈ 1√N
·√
θ
μ·[h(β)− β
].
� P{Ab} ∝ E[Wq] , both order 1√N
:
P{Ab}E[Wq]
= θ (≈ g(0) > 0).
73 94
QED Theory vs. Data: P(Wq > 0)
IL Telecom; June-September, 2004
� 2205 half-hour intervals (13 summer weeks, week-days)� Erlang-A approximations for the appropriate μ/θ ≈ 3
74 95
Process Limits (Queueing, Waiting)• QN = {QN(t), t ≥ 0} : stochastic process obtained by
centering and rescaling:
QN =QN −N√
N
• QN(∞) : stationary distribution of QN
• Q = {Q(t), t ≥ 0} : process defined by: QN(t)d→ Q(t).
��
�
�
� �
QN(t) QN(∞)
Q(t) Q(∞)
t → ∞
t → ∞
N → ∞ N → ∞
Approximating (Virtual) Waiting Time
VN =√N VN ⇒ V =
[1
μQ
]+(Puhalskii, 1994)
stochastic process
Waiting Time
75 96
QED Q’s in Practice, beyond Call Centers
Traditional Queueing Theory predicts that Service-Quality andServers’ Efficiency must be traded off against each other.
For example, M/M/1 (single-server queue): 91% server’s utilizationgoes with
Congestion Index =E [Wait ]
E [Service]= 10.
68 97
QED Q’s in Practice, beyond Call Centers
Traditional Queueing Theory predicts that Service-Quality andServers’ Efficiency must be traded off against each other.
For example, M/M/1 (single-server queue): 91% server’s utilizationgoes with
Congestion Index =E [Wait ]
E [Service]= 10.
Yet, heavily-loaded queueing systems with Congestion Index = 0.1(Waiting-time one order of magnitude less than Service-time)are prevalent:
� Call Centers: Wait “seconds" for minutes service;� Transportation: Search “minutes" for hours parking;� Hospitals: Wait “hours" in ED for days hospitalization in IW’s.
⇒ QED Systems68 98
QED Intuition: Why P{Wq > 0} ∈ (0, 1) ?
1. Why subtle: Consider a large service system (e.g. call center).� Fix λ and let N ↑ ∞: P{Wq > 0} ↓ 0, P(I > 0) ↑ 1.
76 99
QED Intuition: Why P{Wq > 0} ∈ (0, 1) ?
1. Why subtle: Consider a large service system (e.g. call center).� Fix λ and let N ↑ ∞: P{Wq > 0} ↓ 0, P(I > 0) ↑ 1.� Fix N and let λ ↑ ∞: P{Wq > 0} ↑ 1, P(I > 0) ↓ 0.
76 100
QED Intuition: Why P{Wq > 0} ∈ (0, 1) ?
1. Why subtle: Consider a large service system (e.g. call center).� Fix λ and let N ↑ ∞: P{Wq > 0} ↓ 0, P(I > 0) ↑ 1.� Fix N and let λ ↑ ∞: P{Wq > 0} ↑ 1, P(I > 0) ↓ 0.� ⇒ Must have both λ and N increase simultaneously:� ⇒ (CLT) Square-root staffing: N ≈ R + β
√R(
λ ≈ Nμ− β√
Nμ)
76 101
QED Intuition: Why P{Wq > 0} ∈ (0, 1) ?
1. Why subtle: Consider a large service system (e.g. call center).� Fix λ and let N ↑ ∞: P{Wq > 0} ↓ 0, P(I > 0) ↑ 1.� Fix N and let λ ↑ ∞: P{Wq > 0} ↑ 1, P(I > 0) ↓ 0.� ⇒ Must have both λ and N increase simultaneously:� ⇒ (CLT) Square-root staffing: N ≈ R + β
√R(
λ ≈ Nμ− β√
Nμ)
2. QED Excursions
76 102
Server Networks (w/ A. Senderovic)
ILDUBank January 24, 2010 Agent #043 Shift: 16:00 - 23:45
Inbound Call-Backs
Outgoing
Available Idle
Private Call
Break
84 107
Individual Agents: Service-Duration, Variabilityw/ Gans, Liu, Shen & Ye
Agent 14115
Service-Time Evolution: 6 month Log(Service-Time)
� Learning: Noticeable decreasing-trend in service-duration� LogNormal Service-Duration, individually and collectively
85 108
Individual Agents: Learning, Forgetting, Switching
Daily-Average Log(Service-Time), over 6 monthsAgents 14115, 14128, 14136
Day Index
Mea
n Lo
g(S
ervi
ce T
ime)
0 20 40 60 80 100 120 1404.2
4.4
4.6
4.8
5.0
5.2
5.4
Day Index
Mea
n Lo
g(S
ervi
ce T
ime)
a 102−day break
0 20 40 60 80 1004.
44.
64.
85.
05.
25.
45.
6Day Index
Mea
n Lo
g(S
ervi
ce T
ime)
switch to Online Banking after 18−day break
0 50 100 150
4.5
5.0
5.5
6.0
86 109
Individual Agents: Learning, Forgetting, Switching
Daily-Average Log(Service-Time), over 6 monthsAgents 14115, 14128, 14136
Day Index
Mea
n Lo
g(S
ervi
ce T
ime)
0 20 40 60 80 100 120 1404.2
4.4
4.6
4.8
5.0
5.2
5.4
Day Index
Mea
n Lo
g(S
ervi
ce T
ime)
a 102−day break
0 20 40 60 80 1004.
44.
64.
85.
05.
25.
45.
6Day Index
Mea
n Lo
g(S
ervi
ce T
ime)
switch to Online Banking after 18−day break
0 50 100 150
4.5
5.0
5.5
6.0
Weakly Learning-Curves for 12 Homogeneous(?) Agents
5 10 15 20
34
56
Tenure (in 5−day week)
Ser
vice
rate
per
hou
r
86 110
Tele-Service Process (Beyond present SEE Data)
RetailService(IsraeliBank)
StatisticsORIEPsychol.MIS
START
Hello14 / 20
I.D.24 / 23Request
15 / 8
Stock17 / 21
Question14 / 20
Password creation62 / 42
Processing49 / 24
Confirmation29 / 9
Answer32 / 19
END202/190
Dead time18 / 17
Paperwork22 / 12
End of call5 / 3
Credit34 / 32
Others21 / 21
Checking21 / 9
1
0.65
0.050.27
0.950.03
0.62
0.29
0.17
0.28
0.17
0.11
0.05
0.05 0.17
0.23 0.08
0.38
0.15
0.15
0.93
0.14
0.03
0.5
0.03 0.26
0. 4
0.23
0.590.09
0.05
0.67
0.11
0.17
0.67
0.330.7
0.25
0.66
0.43
0.57
0.130.2
0.93
0.04
0. 6
Password creation62 / 42
0.67
0.33
STDAVG
87 111
Technion Research Impact: An Example
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N Gans, G Koole, A Mandelbaum - Manufacturing and service operations …, 2003 - Citeseer � The Wharton School, University of Pennsylvania,Philadelphia, PA 19104, USA [email protected] ... † Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands [email protected] ... ‡ Industrial Engineering and ... Cited by 455 - Related articles - View as HTML - All 32 versions
[PDF] Telephone call centers: Tutorial, review, and research prospects psu.edu [PDF]
O Garnet, A Mandelbaum, M … - Manufacturing & Service …, 2002 - iew3.technion.ac.il ABSTRACT. The most common model to support workforce management of telephone call centers is the M/M/N/B model, in particular its special cases M/M/N (Erlang C, which models out busy-signals) and M/M/N/N (Erlang B, disallowing waiting). All of these models lack a ... Cited by 245 - Related articles - View as HTML - All 18 versions
[PDF] Designing a call center with impatient customers technion.ac.il [PDF]
L Brown, N Gans, A Mandelbaum, A Sakov, H … - Journal of the American …, 2005 - ASA A call center is a service network in which agents provide telephone-based services. Customers who seek these services are delayed in tele-queues. This article summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history ... Cited by 205 - Related articles - All 41 versions
Statistical Analysis of a Telephone Call Center psu.edu [PDF]
S Borst, A Mandelbaum, MI Reiman - Operations research, 2004 - JSTOR CWI, P. O. Box 94079, 1090 GB Amsterdam, The Netherlands, and Bell Labs, Lucent Technologies, Murray Hill, New Jersey 07974-0636, [email protected] Avi Mandelbaum Faculty of Industrial Engineering and Management, Technion, Haifa 32000, Israel, avim@tx. ... Cited by 156 - Related articles - BL Direct - All 19 versions
Dimensioning large call centers bell-labs.com [PDF]
G Koole, A Mandelbaum - Annals of Operations Research, 2002 - Springer ... the modern call center is a complex socio-technical system. It thus enjoys central features that
Queueing models of call centers: An introduction psu.edu [PDF]
2,510,000.
call centers
N Gans, [ ]
O Garnet, [ ]
L Brown,
91 113
Data-Based Creation ServNets: some Technicalities
� ServNets = QNets, SimNets, FNets, DNets� Graph Layout: Adapted from but significantly extends Graphviz
(AT&T, 90’s); eg. edge-width, which must be restricted topoly-lines, since there are “no parallel Bezier (Cubic) curves(Bn(p) = EpF [B(n, p)], 0 ≤ p ≤ 1)
� Algorithm: Dot Layout (but with cycles), based on Sugiyama,Tagawa, Toda (’81): “Visual Understanding of HierarchicalSystem Structures"
33 114
Data-Based Creation ServNets: some Technicalities
� ServNets = QNets, SimNets, FNets, DNets� Graph Layout: Adapted from but significantly extends Graphviz
(AT&T, 90’s); eg. edge-width, which must be restricted topoly-lines, since there are “no parallel Bezier (Cubic) curves(Bn(p) = EpF [B(n, p)], 0 ≤ p ≤ 1)
� Algorithm: Dot Layout (but with cycles), based on Sugiyama,Tagawa, Toda (’81): “Visual Understanding of HierarchicalSystem Structures"
� Draws data directly from SEELab data-bases:� Relational DBs (Large! eg. USBank Full Binary = 37GB, Summary
Tables = 7GB)� Structure: Sequence of events/states, which (due to size)
partitioned (yet integrated) into days (eg. call centers) or months(eg. hospitals)
� Differs from industry DBs (in call centers, hospitals, websites)
33 115
Skills-Based Routing in Call CentersEDA and OR, with I. Gurvich and P. Liberman
Mktg. ⇒
OR ⇒
HRM ⇒
MIS ⇒
20 119