Simulation enables the study of complex system. Simulation is a good approach when analytic study of a system is not possible or very complex. Informational, organizational, and environmental changes can be simulated. The knowledge gained in designing a simulation model may be of great value toward suggesting improvement in the system under investigation. Simulation can be used to experiment with new designs or policies prior to implementation (what if scenarios). Experiments can be very expensive , dangerous … The modern system is so complex that the interactions can be treated only through simulation.

When and Why to use Simulations?

when the problem can be solved using common sense

when the problem can be solved analytically

when it is easier to perform direct experiments

when the costs exceed the savings

when the resources or time are not available

when the ability to verify and validate the model is very limited

when the system behavior is too complex or cannot be defined

When Simulation Cannot be Used?

Role of Computers in Simulation• Computers are critical in simulating complex tasks• Three types of computer programming languages are

available to help the simulation process• General-purpose languages • Special-purpose simulation languages

1. These require less programming2. Are more efficient and easier to check for errors3. Have random number generators built in

• Pre-written simulation programs built to handle a wide range of common problems

• Excel and add-ins can also be used for simulation problems

• Using simulation, a manager should1. Define a problem2. Introduce the variables associated with the problem3. Construct a numerical model4. Set up possible courses of action for testing5. Run the experiment6. Consider the results7. Decide what courses of action to take

Process of Simulation

Process of SimulationDefine Problem

Introduce Important Variables

Construct Simulation Model

Specify Values of Variables to Be Tested

Conduct the Simulation

Examine the Results

Select Best Course of Action

Simulation Study (detailed vision)

1- Problem formulation: Every study

should begin with a statement of the

problem

2- Setting of objectives and overall

project plan: The objectives indicate

the questions to be answered by

simulation.

3- Model conceptualization: The

construction of a model of a system is

probably as much art as science

Simulation Study (detailed vision)

4- Data collection: There is a

constant interplay between the

construction of the model and the

collection of the needed input data

[Shannon, 1975]. As the

complexity of the model changes,

the required data elements may

also change.

5- Model translation: the model

must be entered into a computer-

recognizable format.

6- Verification: Is the computer

program performing properly?

7- Validation: Does the simulation

model replicate this system measure?

Simulation Study (detailed vision)

8- Experimental design: The

alternatives that are to be simulated

must be determined

9- Production runs and analysis:

Production runs, and their

subsequent analysis, are used to

estimate measures of performance

for the system designs that are being

simulated.

Simulation Study (detailed vision)

10- More runs? determines if

additional runs are needed and what

design those additional experiments

should follow.

11- Documentation and Reporting.

12- Implementation.

Simulation Study (detailed vision)

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Discrete Event Simulation

• Definition• Time-Advance Mechanisms • Components and Organization of a Discrete -Event

Simulation Model– Components– Logic Organization

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Definitions

• Discrete-event simulation concerns the modeling of a system as it evolves over time by a representation in which the state variables change instantaneously at separate points in time. Or the system can 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 or idle),

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 the completion of service for a customer, which results in the customer’s departure.

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Time-Advance Mechanisms• 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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Time-Advance Mechanisms• More on next-event time advance

– Initialize simulation clock to 0– Determine times of occurrence of future events – event list– Clock advances to next (most imminent) event, which is

executed• Event execution may involve updating event list

– Continue until stopping rule is satisfied (must be explicitly stated)

– Clock “jumps” from one event time to the next, and doesn’t “exist” for times between successive events … periods of inactivity are ignored

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Example 1.2• Notations: – ti: time of arrival of the ith customer (t0=0)

– Ai: interarrival time between (i-1)st and ith arrivals of customers

– Si : time that server actually spends serving ith customer (exclusive of customer’s delay in queue)

– Di : delay in queue of ith customer

– Ci : time that ith customer completes service and departs

– ei : time of occurrence of ith event of any type (ith value the simulation clock takes on, excluding the value )

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e0 e1 e2 e3 e4 e5

0 t1 t2 c1 t3 c2

A1 A2 A3

S1 S2

Time

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Components and Organization of a Discrete-Event Simulation Model

• Components (10) 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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Continue... Initialization routine: A subprogram to initialize the

simulation model at time 0 Timing routine: A subprogram that determines the

next 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)

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Continue... Library routines: A set of subprograms used to

generate random observations from probability distributions that were determined as part of the simulation model

Report generator: A subprogram that computes estimates (from the statistical counters) of the desired measures of performance and produces a report when the simulation ends

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Continue... Main program: A subprogram that invokes the timing

routine to determine the next event and then transfers control to the corresponding event routine to update the system state appropriately. The main program may also check for termination and invoke the report generator when the simulation is over.

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Start

1. Set simulation clock=02. Initialize system state and statistical counters3. Initialize event list

0. Invoke the initialization routine

1. Invoke the timing routine2. Invoke event routine

1. Determine the next event type, say, i2. Advance the simulation clock

1.Update system state2.Update statistical counters3.Generate future events and add to event list

Repeatedly

Initialization routine Main program Time routine

Event routine i

Generate randomvariates

Library routines

Issimulation

over?

1. Compute estimates of interest2. Write report

Stop

Report generator

10

2

i

No

Yes