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Chapter-1 :Basic Simulation Modeling

1.1The nature of simulation

1.2 Systems, Models and Simulation

1.3 Discrete-Event Simulation1.3.1 Time-Advance Mechanisms

1.3.2 Components and organization of

Discrete Event Simulation Model

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1.1 The Nature of

Simulation(( Conceptions

Application areas

Academic level Impediments

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Conceptions Simulation course is about techniques for using computers to

imitate or simulate the operations of various kinds of realworld facilities or processes

System: the facility or process of interest

Model(): a set of assumptions about how the systemworks, which usually take the form of mathematical or logicalrelationships, constitute a model that is used to try to gain

more understanding of how the corresponding system

behaves.

Analytic solution(): to obtain exact information onquestions of intresets.

Simulation)(:use a computer to evaluate a modelnumerically, and data are gathered in order to estimate the

desired true characteristics of the model.

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Example

a manufacturing company contemplates

building a large extension onto one of its

plants, but is not sure if the potential gain

in productivity would justify the

construction cost.

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Application areas of Simulation

Designing and analyzing manufacturing systems

evaluating military weapons systems or their logistics

requirements

determining hardware requirements or protocols for

communication networks

Determining hardware and software requirements for acomputer system

Designing and operating transportation systems such as

airports, freeways, ports and subways

Evaluating designs for service organizations such as callcenters, fast-food restaurants, hospitals, and post offices

Reengineering of business processes

Determining ordering polices for an inventory system

Analyzing financial or economic systems

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Academic level

Winter Simulation Conference (600-700 people

every year)

It isone of the three important operations-

research techniques (in serveys related to theuse of operations research techniques: math

programming, statistics, simulation)

The second only to math programming among

13 techniques considered (in 1294 papers from

the journal Interfaces from 1970 through 1992)

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Impediments Models used to study large-scale systems tend

to be very complex, and writing computerprograms to execute them can be an arduous

task indeed. (excellent software products )

Large amount of computer time is sometimes

required. (cheaper and faster computer)

An unfortunate impression that simulation is just

an exercise in computer programming, albeit a

complicated one. (attitude, simulationmethodology)

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1.2 Systems, Models and Simulation System is defined to be a collection of entities, e.g., people or

machines, which act and interact together toward theaccomplishment of some logical end.

System depends on the objectives of a particular study.

State of a system: collection of variables) (necessary to describe a system at a particular time, relativeto the objectives of a study. (the number of busy tellers, the

number of customers in the bank, the time of arrival of each

customer in the bank)

discrete system: the state variables change instantaneously )at separated points in time. (a bank, e.g., the number of customers in)the bank)

continuous system: the state variables change continuously)

) with respect to time. (an airplane moving through the air, e.g.,position and velocity)

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Continue... Study on a system: try to gain some insight

into the relationships among variouscomponents, or to predict performance under

some new conditions being considered.

Ways to study a system

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System

Experimentwith the

actual system

Physical

model

Analytical

solutionSimulation

Experimentwith a model

of the system

Mathematical

model

Figure 1.1 Ways to study a system

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Example If one wants to study on a bank to determine

the number of tellers needed to provideadequate service for customers who want

just to cash a check or make a savings

deposit, the system can be defined to bethat portion of the bank consisting of the

tellers and the customers waiting in line or

being served.

If the loan officer and the safety deposit

boxes are to be included, the definition of

the system must be expanded in an

obvious way.

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Classification of simulation models

Static vs. dynamic

Deterministic vs. stochastic

Continuous vs. discrete

Most operational models are dynamic,

stochastic, and discrete will be called

discrete-event simulation models

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1.3 Discrete-Event Simulation Discrete-event simulation concerns the

modeling of a system as it evolves overtime by a representation in which the state

variables change instantaneously at

separate points in time. Or the systemcan change at only a countable number of

points in time.

Event is defined as an instantaneous

occurrence that may change the state of

the system.

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Example 1.1 Single-server queuing system: a

barbershop, to estimate the (expected)average delay in queue (line) of arriving

customers

State variables: the status of the server (busy oridle), the number of customers waiting in queue

to be served, the time of arrival of each person

waiting in queue.

Events: the arrival of a customer and thecompletion of service for a customer, which

results in the customers departure.

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1.3.1.Time-Advance Mechanism Simulation clock: the variable in a simulation model

that gives the current value of simulated time. to keep track of the current value of simulated time as the

simulation proceeds

to advance simulated time from one value to another

Advancing the simulation clock

next-event time advance (mostly used)

fixed-increment time advance (a special case of the first)

Next-event time-advance approach simulation clock is initialized to zero

the times of occurrence of future events are determined.

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Example 1.2Notation:

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e0 e1 e2 e3 e4 e5

0 t1 t2 c1 t3 c2

A1 A2 A3

S1 S2

Time

Figure 1.2 The next-event time-advance approach illustrated for the single-

server queuing system

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1.3.2 Components and Organization of

a Discrete -Event Simulation Model

Components Systems state: The collection of state variables

necessary to describe the system at a particular

time

Simulation clock: A variable giving the current

value of simulated time

Event list: A list containing the next time when

each type of event will occur Statistical counters: Variables used for storing

statistical information about system performance

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Initialization routine: A subprogram to initialize the

simulation model at time 0

Timing routine: A subprogram that determines thenext event from the event list and then advances

the simulation clock to the time when that event is

to occur

Event routine: A subprogram that updates the

system state when a particular type of event occurs

(there is one event routine for each event type)

Library routines: A set of subprograms used togenerate random observations from probability

distributions that were determined as part of the

simulation model

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Report generator: A subprogram that computes

estimates (from the statistical counters) of thedesired measures of performance and

produces a report when the simulation ends

Main program: A subprogram that invokes the

timing routine to determine the next event andthen transfers control to the corresponding

event routine to update the system state

appropriately. The main program may also

check for termination and invoke the reportgenerator when the simulation is over.

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Start

1. Set simulation

clock=0

2. Initialize system state

and statistical counters

3. Initialize event list

0. Invoke the initialization routine

1. Invoke the timing routine2. Invoke event routine

1. Determine the next

event type, say, i

2. Advance thesimulation clock

1.Update system state

2.Update statistical counters

3.Generate future events and add toevent list

Repeatedly

Initialization routine Main program Time routine

Event routine i

Generate random

variates

Library routines

Issimulation

over?

1. Compute estimates of interest

2. Write report

Stop

Report generator

10

2

i

No

Yes