Introduction to Simulation and Modelling, Summaries of Mathematical Modeling and Simulation

Download Introduction to Simulation and Modelling and more Summaries Mathematical Modeling and Simulation in PDF only on Docsity!

:Chapter 1

Objective / Introduction to

Simulation

SIMULATION AND MODELLING

Course outlines

Introduction to Basic simulation models

Modelling and Simulation

Probability in Simulation

• (^) Discrete-Event Simulation
• (^) Continuous System Simulatio n
• (^) Random number

Other simulation models

Simulation for Aircraft Model

• (^) Queuing System Simulation

Introduction to Simulation

• (^) Simulation
  • (^) the imitation of the operation of a real-world process or system

over time

• (^) to develop a set of assumptions of mathematical, logical, and

symbolic relationship between the entities of interest, of the

system.

• (^) to estimate the measures of performance of the system with the

simulation-generated data

• (^) The behavior of a system as it evolves over time is studied by

developing a simulation model.

Real-world

process (^) concerning the behavior of a system

A set of assumptions

Modeling

& Analysis

To simulate any system we need at first to build a model

for that system then simulate this model

Simulating

Simulation allows us to:

• (^) Model complex systems in a detailed way
• (^) Describe the behavior of systems
• (^) Construct theories or hypotheses that account for the

observed behavior

• (^) Use the model to predict future behavior, that is, the

effects that will be produced by changes in the system

• (^) Analyze proposed systems

Why we need simulation?

Because the real system is:

• too cumbersome (رهق طيئم, ب , م عقد – قيل ث )
• (^) too costly
• (^) too dangerous
• (^) too slow

Goal of modeling and simulation

A model : can be used to investigate a wide verity of “what

if” questions about real-world system.

 Potential changes to the system can be simulated and

predicate their impact on the system.

 Find adequate parameters before implementation

So simulation can be used as

 Analysis tool for predicating the effect of changes

 Design tool to predicate the performance of new system

(It is better to do simulation before Implementation).

Simulation can be used to experiment with new designs

or policies prior to implementation, so as to prepare for

what may happen.

Simulation can be used to verify analytic solutions.

By simulating different capabilities for a machine,

requirements can be determined.

Animation shows a system in simulated operation so

that the plan can be visualized.

Simulation can be used as a pedagogical device to

reinforce analytic solution methodologies

When Simulation is the Appropriate Tool (2)

When Simulation is not Appropriate

• 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 simulation costs exceed the savings.
• (^) When the resources or time are not available.
• When system behavior is too complex or can’t be defined.
• (^) When there isn’t the ability to verify and validate the model.

Disadvantages of Simulation

1. Can be expensive and time consuming
2. Managers must choose solutions they want to try

(“what-if” scenarios)

3. Each model is unique
4. Model building is an art as well as a science. The

quality of the analysis depends on the quality of the

model and the skill of the

5. Simulation results are sometimes hard to interpret.
6. Should not be used when an analytical method

would provide for quicker results.

definition :

System is a collection of entities (people, parts, messages,

machines, servers, …) that act and interact together toward some

end (Schmidt and Taylor, 1970)

• In practice, depends on objectives of study
• (^) Might limit the boundaries (physical and logical) of the

system

System

Components of a System

Entity : an object of interest in the system.

Attribute : a property of an entity.

Activity : a time period of specified length.

State : the collection of variables necessary to describe

the system at any time, relative to the objectives of the

study.

Event : an instantaneous occurrence that may change the

state of the system.

Endogenous : to describe activities and events occurring

within a system.

Exogenous : to describe activities and events in an

environment that affect the system.

:DISCRETE AND CONTINUOUS SYSTEMS

• DISCRETE SYSTEMS:

is one in which the state variable(s) change only at a

discrete set of points in time.

An example: Is the bank

• CONTINUOUS SYSTEMS:

• (^) is one in which the state variable(s) change continuously.
• (^) An example: water dam.

SYSTEM Entities Attributes Activities Events State variables

Banking Customers Checking

account

balance

Making deposits Arrival;

departure

Number of busy

tellers; number of

Customers waiting

Railways Riders Origination

destination

Traveling Arrival at

Station;

Arrival at

destination

Number of riders

waiting at each

station; number of

riders in transit

Production Machines Speed; capacity

breakdown rate

Welding stamping Breakdown Status of machines

( busy , idle, or

down)

Communications Messages Length;

destination

Transmitting Arrival at

destination

Number waiting to

be transmitted

Inventory Warehouse Capacity Withdrawing Demand Levels of inventory ;

backlogged

demands

EXAMPLE OF SYSTEM AND COMPONENTS:

The Process of Simulation