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- Al-Imam Mohammad Ibn Saud University

CS433Modeling and SimulationLecture 09 Part

02Discrete Events Simulation

http//10.2.230.104040/akoubaa/cs433/

Dr. Anis Koubâa

27 Dec 2008

Outline

- Basic Concepts of Simulation
- Why using simulations?
- Advantages and drawback of simulations
- Types of simulations
- Steps in a simulation study
- Discrete Event Simulation (DES)

Basic Concepts

- Simulation It is a numerical technique for

conducting experiments with certain types of

mathematical models describing the behavior of

complex systems on a digital computer over

extended periods of time (Naylor 1971) - In a Simulation, a computer is used to evaluate a

model numerically, and then gather data in order

to estimate the desired characteristics of the

model. - Example A manufacturing firm that is thinking to

build a large extension onto one of its plants. - Question Will the potential gain in productivity

justify the construction cost? - Problem It would not be cost effective to build

the extension and then remove it later if it does

not work out. - Solution Simulation!

When and Why to use Simulations?

- 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 Simulation Cannot be Used?

- 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

Application Areas of Simulation

Advantages/Drawbacks of Simulation

- Advantages
- Adequate for assessing models too complicated

for analytical or numerical study - New policies, decision rules, etc., can be

explored without disrupting ongoing operations of

the real system - What if scenarios can be analyzed which are

useful in the design of new systems. - Drawbacks
- Sometimes very time consuming/costly
- To analyze a certain problem, better methods

than simulation may exist - Simulations provide random output
- (lots of misinterpretation possible).

Types of Simulation

- Static vs. Dynamic
- Does time have a role in the model?
- Continuous-change vs. Discrete-change
- Can the state change continuously or only at

discrete points in time? - Deterministic vs. Stochastic
- Is everything for sure or is there uncertainty?
- Most operational models
- Dynamic, Discrete-change, Stochastic

Types of Simulation

Concepts in Discrete Event Simulation

Steps of a Simulation Study

Steps in Simulation Study

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

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

Steps in Simulation Study

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?

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.

Steps in Simulation Study

10- More runs? determines if additional runs are

needed and what design those additional

experiments should follow.

11- Documentation and Reporting.

12- Implementation.

Discrete-Event Simulation

Outline

- Time-stepped implementation critique
- Discrete event fundamentals
- Simulation engine
- Example Airport Simulation
- Discrete event simulation critique

State Variables

queue

customer

server

- State
- InTheAir number of aircraft either landing or

waiting to land - OnTheGround number of landed aircraft
- RunwayFree Boolean, true if runway available

Time Step Implementation

- / ignore aircraft departures /
- Float InTheAir aircraft landing or waiting to

land - Float OnTheGround landed aircraft
- Boolean RunwayFree True if runway available
- Float NextArrivalTime Time the next aircraft

arrives - Float NextLanding Time next aircraft lands (if

one is landing) - For (Now 1 to EndTime) / time step size is

1.0 / - if (Now gt NextArrivalTime) / if aircraft

just arrived / - InTheAir InTheAir 1
- NextArrivalTime NextArrivalTime

RandExp(A) - if (RunwayFree)
- RunwayFree False
- NextLanding Now RandExp(L)
- if (Now gt NextLanding) / if aircraft just

landed / - InTheAir InTheAir - 1
- OnTheGround OnTheGround 1

Problems With Time Step Approach

- State changes may occur between time steps
- Use small time steps to minimize error
- Multiple state changes within the same time step

may be processed in the wrong order - Solvable by ordering state changes within time

step (this imposes more work) - Inefficient
- Many time steps no state changes occur,

especially if small time steps

Discrete Event Simulation

- Discrete Event Simulation computer model for a

system where changes in the state of the system

occur at discrete points in simulation time. - Fundamental concepts
- System state (state variables)
- State transitions (events)
- Each event has a timestamp indicating when it

occurs. - A DES computation can be viewed as a sequence of

event computations, with each event computation

is assigned a (simulation time) time stamp - Each event computation can
- Modify state variables
- Schedule new events

Discrete Event Simulation Computation

- Example air traffic at an airport
- Events aircraft arrival, landing, departure

arrival 800

schedules

departure 915

arrival 930

landed 805

schedules

simulation time

- Events that have been scheduled, but have not

been simulated (processed) yet are stored in a

pending event list - Events are processed in time stamp order why?

Discrete Event Simulation System

Events

- An event must be associated with any change in

the state of the system - Airport example
- Event 1 Aircraft Arrival (InTheAir, RunwayFree)
- Event 2 Aircraft Landing (InTheAir,

OnTheGround, RunwayFree) - Event 3 Aircraft Departure (OnTheGround)

Event-Oriented World View

Example Air traffic at an Airport

- Model aircraft arrivals and departures, arrival

queuing - Single runway for incoming aircraft, ignore

departure queuing - L mean time runway used for each landing

aircraft (exponential distrib.) - G mean time on the ground before departing

(exponential distribution) - A mean inter-arrival time of incoming aircraft

(exponential distribution) - States
- Now current simulation time
- InTheAir number of aircraft landing or waiting

to land - OnTheGround number of landed aircraft
- RunwayFree Boolean, true if runway available
- Events
- Arrival denotes aircraft arriving in air space

of airport - Landed denotes aircraft landing
- Departure denotes aircraft leaving

Arrival Events

- Arrival Process New aircraft arrives at

airport. - If the runway is free, it will begin to land.
- Otherwise, the aircraft must circle, and wait to

land.

A mean interarrival time of incoming

aircraft Now current simulation time InTheAir

number of aircraft landing or waiting to

land OnTheGround number of landed

aircraft RunwayFree Boolean, true if runway

available

- Arrival Event
- InTheAir InTheAir1
- Schedule Arrival event _at_ Now RandExp(A)
- If (RunwayFree)
- RunwayFreeFALSE
- Schedule Landed event _at_ Now RandExp(L)

Landed Event

Landing Process An aircraft has completed its

landing.

L mean time runway is used for each landing

aircraft G mean time required on the ground

before departing Now current simulation

time InTheAir number of aircraft landing or

waiting to land OnTheGround number of landed

aircraft RunwayFree Boolean, true if runway

available

- Landed Event
- InTheAirInTheAir-1
- OnTheGroundOnTheGround1
- Schedule Departure event _at_ Now RandExp(G)
- If (InTheAirgt0)
- Schedule Landed event _at_ Now RandExp(L)
- Else
- RunwayFree TRUE

Departure Event

Departure Process An aircraft now on the ground

departs for a new destination.

Now current simulation time InTheAir number of

aircraft landing or waiting to land OnTheGround

number of landed aircraft RunwayFree Boolean,

true if runway available

- Departure Event
- OnTheGround OnTheGround - 1

Execution Example

Output Statistics

- Compute
- The maximum number of aircraft that will be on

the ground at one time - Average time an aircraft must wait before they

are allowed to land - Solution
- Maximum on ground
- Variable for airport indicating number currently

on ground - Maximum on the ground so far
- Wait time
- Variables for airport indicating total wait time,

number of aircraft arrivals - State variable for each aircraft indicating the

arrival time

Discrete Event Simulation

- Avoids problems of time stepped execution
- Error when events lie between time steps
- Time steps with no events
- But
- Priority queue (pending event list) introduces

some new computational overhead - What about events with the same time stamp?
- More important than one might initially think!

Summary

- Methodology
- Important to have a reasonably clear conceptual

and specification model before moving to

implementation (computational model) - Key concepts state variables and changes in

state - Simulation engine largely independent of

application - Simulation model state variables and code to

modify state - Time stepped vs. event driven execution
- In principle, either can be used to model system
- Discrete-event simulation approach more commonly

used to model queuing systems

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