2104612 Computer Simulation Introduction

W I P A W E E T H A R M M A P H O R N P H I L A S

W I P A W E E . T @ C H U L A . A C . T H

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Computer SimulationAn Introduction

System Analysis


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System

Experiment with

actual system

Physical model

MathematicalModel

Analyticalsolution

Simulation

Experiment With model

A system is a collection of component and their relationship

What is simulation?


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A broad collection of methods and applications to mimic the behavior of real system, usually on a computer

What’s Being Modeled?


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A manufacturing plant

A bank or other personal-service operation

A distribution network of plants, warehouses, transportation links

A freeway system of road segments, interchanges, controls, and traffic

A theme park

Etc.

Benefits of using simulation (1)


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Evaluates the system’s behavior under a variety of assumed conditions.

Allows the analyst to draw inferences about new systems without building them, or make changes to existing systems without disturbing them.

Allows the analyst to draw conclusions about expected system behavior, and about the likelihood of departures from expected behavior.

Benefits of using simulation (2)


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Allows decision-makers to visualize the operation of a new or existing system under a variety of conditions, using computer animation.

Provides understanding of how various components interact with each other and how they affect overall

system performance.

Limitations of simulation


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Does not provide explicit relationships b/w system input (decision variables) and system output (performance criteria).

Does not provide optimal solutions- only provides the results of what-if questions, from which solutions are inferred.

May lead to incorrect conclusions if not used properly (for example, if the level of detail is too low, or if the run length is too short).

Requires a skilled analyst to be used effectively.

System characteristics


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Different kinds of simulations (1)


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Static vs. Dynamic⚫ Static: time plays no role (Monte Carlo)

⚫ Dynamic: model represents a system as it evolves over time

Continuous vs. Discrete ⚫ Continuous simulation concerns with systems whose

parameters vary continuously with respect to space and/or distance. Ex: an airplane moving through the air

⚫ A discrete system concerns with systems whose parameters experience abrupt changes at discrete points in time.

Different kinds of simulations (2)


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Deterministic vs. Stochastic⚫ Deterministic: model does not contain any probabilistic

⚫ Stochastic: model has at least one random component

⚫ In discrete event simulation, we calculate the solution for every change of events.

⚫For example, in a queuing system, we calculate the system when an entity arrives, or when an entity leaves the system

Discrete Event Simulation

Key Modeling Processes


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Real World(Problem)

ConceptualModel

ComputerModel

Solutions/Understanding

Conceptual Model


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Develop an understanding of the problem situation

Determine the modeling objectives

Design the conceptual model: inputs, outputs, and model content

Collect and analyze the data required to develop the model

Model Coding


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General-purpose languages (C, Fortran, etc).

Where it all began (origins of simulation).

Use is complicated and time-consuming.

Impractical for large-scale model development.

Simulation languages (SIMAN, GPSS, SLAM, etc.)

Very robust –can be applied to any problem settings.

Automates much of the logic required in a C or Fortran program.

Much easier to learn and to used.

Simulators (ARENA, PRO-MODEL, Simio etc.)

Very easy to learn and use.

Experimentation


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What-if analysis

Key issues⚫ Obtaining sufficiently accurate results

⚫ Performing a thorough search of potential solutions (searching the solution space)

⚫ Testing the robustness of the solution (sensitivity analysis)

Implementation


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Implementing the finding from a simulation study in the real world

Implementing the model rather than the finding

The Model-Building Process


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1. Define the problem and its goals.

2. Gather data

3. Develop a preliminary project plan

4. Formulate the simulation model

5. Run the model

6. Verify the model (does it simulate the model right?)

7. Validate the model (does it simulate the right model?)

8. Analyze the results

9. Draw conclusion.

10. Recommend alternatives to the decision maker.

An Example Simulation (A computer IT help desk)

Help-desk operator has two states Busy helping someone

Waiting for a call to come in

Events Customer starts describing problem to help desk

Customer completes conversation


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Working it out

Simulation starts at t = t0 = 0

First customer arrives at t1, simulation time now t = t0 + t1

Help desk requires ts to resolve the issue

First simulation leaves at t = t0 + t1 + ts

Second customer arrives at t2

If t2 < t0 + t1 + ts, then customer must wait

It t2 > t0 + t1 + ts, then customer starts service


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Simulate a bank system


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At a bank, let arrivals occurring at times 0.4, 1.6, 2.1, 3.8, 4.0, 5.6, 5.8, and 7.2.

Departures (service completions) occur at times 2.4, 3.1, 3.3, 4.9, and 8.6, and the simulation ends at time 8.6

Compute ⚫ the expected average delay

⚫ the expected average number of customers in the queue

⚫ the expected utilization of the server


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Simulation Model (Cinema)

Conceptual Modeling--Problem Situation (1)


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Got complaints about the telephone enquiries and booking service

The telephone system was installed at the time the cinema was opened. With the rising demand the queues are now often full; especially on Saturday.

Customer either balk, or wait for some time and hang up

The 3 booking clerks are lambasted by irate customers who have waited up to 15 min or more

Conceptual Modeling--Problem Situation (2)


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The manager is concerned about the loss of goodwill. He has decided to purchase and install a digital system.

Call router(4 lines)

Information(4 lines)

CSR(4 lines)

Ticket sales(4 lines)

Call arrival

Conceptual Modeling-- Modeling Objectives


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Determine the number of resources (info lines and ticket sales lines) required so that less than 5% of calls are lost on busy days and total waiting time is less than 2 minutes for 80% of calls (mean less than 1 minute)

Determine the maximum capacity of the system (number of calls that can be handled) while maintaining service level

CSR staff requirements can be determined in second phase of work

Conceptual Modeling-- Project Objectives


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Time-scale: a final report must be available in 3 weeks

Nature of model display: 2D schematic, showing flow of calls through the system

Nature of model use: by modeler

Conceptual Modeling-- Model inputs and outputs


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Experimental factors⚫ Number of information lines (4,6,8)

⚫ Number of ticket sales lines (4,6,8)

⚫ Call arrival rate

Responses (to determine achievement)⚫ Percentage of lost calls

⚫ Percentage of completed calls with a total waiting time of less than 2 minutes

⚫ Histogram of total waiting time for all completed calls including mean, s, max, min

Conceptual Modeling-- Model inputs and outputs


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Responses ( to determine reasons for failure)⚫ Percentage of lost calls by area

⚫ Queue sizes

⚫ Resource utilization

⚫ Time-series of calls arriving at call router by hour

⚫ Time-series of mean resource utilization by hour

⚫ Time-series of mean size of each queue by hour

Conceptual Modeling-- Model Content

Component In/Ex Justification

Calls In Flow through the telephone system

Service process

Call router

Information

Ticket sales

CSR

In

In

In

In

In

Statistics on queue and resource utilization

Connects call arrival to service process

Experimental factor

Experimental factor

Affects total waiting time

Queues In Required for waiting time, Q size

CSR staff In Affects total waiting time


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Conceptual Modeling --Model level of detail (1)


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Component Detail In/Ex Comment

Calls Customer inter-arrival time

Rate varying by hour of day

Rate varying by day of week

Inter-arrival time rate fixed

In

Ex

In

Dist. changing parameter every 2hrs

Model busiest

Determine system capacity

Service

Process

Number of lines

Service time

Failure

Routing

In

In

Ex

In

Affects speed of service

Distribution

Rarely occur

Conceptual Modeling --Model level of detail (2)

Component Detail In/Ex Comment

Queues Capacity

Queue priority

Leaving threshold

Individual caller behavior

In

In

In

Ex

Affect balking

Affect WT

Affect lost calls

Not well understood

CSR staff Number

Staff rosters

In

Ex

Represent as total lines available


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Conceptual Modeling -- Assumptions


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Sufficient call router lines

No requirement to increase # CSR lines

Arrival pattern defined in 2-hour slots

Equipment failure occur rarely

Individual customer behavior is not modeled

Historical data is accurate to predict future

Model data -- Calls

Negative exponential distribution

Time of day Mean arrival rate

per hour

Mean inter-arrival time (minutes)

8:00-10:00

10:00-12:00

12:00-14:00

14:00-16:00

16:00-18:00

18:00-20:00

20:00-22:00

120

150

200

240

400

240

150

0.5

0.4

0.3

0.25

0.15

0.25

0.4


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Nature of call: Info 60%, Ticket sales 30%, CSR 10%

Model Data -- Others (1)


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Call Router⚫ Number of lines 4

⚫ Service time Lognormal (location = 0.71, spread =0.04, giving mean = 0.5, SD =0.1)

Information⚫ Number of lines 4

⚫ Service time Erlang (mean = 2, k =5)

⚫ Routing out leave 73%, ticket sales 25%, CSR 2%



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Ticket sales⚫ Number of lines 4

⚫ Service time Lognormal (location = 1.09, spread =0.02, giving mean =3.0, SD =0.4)

⚫ Routing out leave 98%, CSR 2%

CSR

⚫ Number of lines 4

⚫ Service time Erlang (mean 3, k=3)



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Queues⚫ Capacity 10

⚫ Queue priority FIFO

⚫ Leaving threshold time 3 minutes

CSR staff⚫ Number 3

Model Coding


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Verification and Validation -- Deterministic model (1)


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Fixed arrival rate 214 per hour = inter-arrival time 0.28 minutes

Customers leave after receiving their first service

Service time at each point is fixed at mean

Info. 0.6, ticket sales 0.3, CSR lines 0.1

Run simulation model 100 hours with a warm-up period 1 hr

Metric Calculation Router Info. Ticket CSR

Arrival rate per hr (a)

Calls handled per hr (b)

Utilization

Total calls per hr * proportion

60m/service time* #lines

(a)/(b)

214*1.0=214

60/0.5*4

=480

44.58%

214*0.6=128.4

60/2*4

=120

100%

214*0.3=64.2

60/3*4

=80

80.25%

214*0.1=21.4

60/3*3

=60

35.67%

Simulation 44.58% 100% 80.25% 35.67%


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Verification and Validation-- Deterministic model (2)

Experimentation-- Obtaining accurate results


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Model is terminating simulation

There are 3 key output statistics⚫ Percentage of lost calls

⚫ Percentage of calls completed with WT < 2 min

⚫ Mean total waiting time

Initial Condition = 0 call

10 Replications of 14 hours

Experimentation (objective 1)-- Percentage of Lost Calls


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Experimentation (objective 1)-- Time Series of the Percentages of Lost Calls


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Experimentation (objective 1)-- Percentage of completed calls WT< 2 min


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Experimentation (objective 1)-- Mean total waiting time


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Experimentation (objective 1)-- Searching the solution space

4 6 8

4 Scenario 1 Scenario 2 Scenario 3




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Information lines

Tic

ket

sale

s lin

es

Experiment is performed on “blue” scenarios



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4 6 8

4 19.11

(18.20,20.03)

10.84

(10.21,11.47)

6 6.70

(6.21,7.20)

8 11.43

(10.50,12.37)

1.69

(1.25,2.13)

Information lines

Tic

ket

sale

s lin

es



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4 6 8

4 63.23

(60.81,65.66)

79.85

(78.64,81.07)

6 80.23

(78.96,81.51)

8 77.27

(74.82,79.72)

90.75

(89.09,92.41)

Information lines

Tic

ket

sale

s lin

es



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4 6 8

4 1.45

(1.37,1.52)

0.85

(0.82,0.89)

6 0.88

(0.83,0.93)

8 0.96

(0.89,1.03)

0.49

(0.44,0.55)

Information lines

Tic

ket

sale

s lin

es

Experimentation-- run scenarios 6 & 8

Results Scenario 6 Scenario 8

Lost calls

Calls with WT < 2

Mean total WT

4.38 (3.78,4.98)

85.86 (84.18,87.53)

0.67 (0.61,0.73)

4.26 (3.97,4.55)

85.36 (84.41,86.31)

0.69 (0.65,0.73)


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•Perform statistical analysis•Scenarios 6 & 8 are not significantly different,but they are significantly different from scenario 9

•The management need to select one scenario

Experimentation (objective 2)


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Scenario 9 is used

Sensitivity Analysis is performed ⚫ Increase arrival rate in steps of 5% to 40%



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Building Model: A barbershop

⚫ Customers visit a barbershop for a haircut. The inter-arrival time is exponentially distributed with the average of 10 min. The barber takes 8-10 min uniformly distributed for each haircut. Simulate the system for 200 min❑ How many customers can be processed?❑ What is the average num of customers waiting to get a haircut?

What is the maximum?

❑ What is the average time spent by a customer in the salon?❑ What is the utilization of the barber

Documents

2104612 Computer Simulation Introduction