Modeling & Simulation: An Introduction Some slides in this presentation have been copyrighted to Dr....

Modeling & Simulation: An Introduction

Some slides in this presentation have been copyrighted to Dr. Amr Elmougy

© Tallal Elshabrawy

Systems

Systems:

A group of objects joined together in some regular interaction or interdependence towards the accomplishment of some purpose.

2


Systems

Systems Environment:

A system is affected by changes that occur outside its boundaries. Such changes are said to occur in the system environment

The boundary between the system and its environment depend on the purpose of the study

3

Boundary

System Environment

i/p

o/p

© Tallal Elshabrawy 4

System Components

System

Entity

Attribute

StateActivity

Event

Object of interest in the system

Property of an entity

Collection of variables necessary to describe the system at a particular time,

An action that takes place over a period of specified length and changes the state of the system

An instantaneous occurrence that may change the state of the system


System Components Example

Queuing System

Packet

Entity

Length, Destination

Attribute

Nof Packets

State

FIFO

Activity

Packet Arrival

Event


Discrete Continuous

State variables change

instantaneously at separated points in time

State variables may change

constantly with respect to time

Types of Systems

Slotted ALOHA Vs Pure ALOHA


Simulation of Continuous Systems

It is feasible to study continuous systems analytically

mathematically

However when it comes to simulation it is challenging.

Solutions: Approximate continuous system as a discrete event

simulation (Discretization)

Event-Driven Simulations


System

Experiment with the

Actual System

Experiment with a Model of the System

Physical Model

Mathematical Model

Analytical Solution Simulation

Approaches to Studying Systems

NETW 707 Modeling & Simulation


Why do we Need Modeling

It is not possible to experiment with the actual system, e.g.: the experiment is destructive

The system might not exist, i.e. the system is in the design stage

In essence it boils down to:

Time Cost Complexity


A model is a representation of a system for the purpose of studying that system

It is only necessary to consider those aspects of the system that affect the problem under investigation

The model is a simplified representation of the system

The model should be sufficiently detailed to permit valid conclusions to be drawn about the actual system

Different models of the same system may be required as the purpose of the investigation changes

Models


Modeling Examples

Grade of Service in 2G Cellular Networks


Modeling Examples

Grade of Service in 2G Cellular Networks

Nof Channels

Aggregate Arrivals

All Servers Busy = Calls Blocked or Delayed


Approaches to Solving Models

Mathematically:

Derivation of equations to answer questions regarding the model.

Derivation Process and Solving could be handled: Analytically: Derives closed form (hopefully concise)

expressions

Numerically: Utilizes the help of numerical approximations (by hand or by programming)

By Simulation: Building a program that tries to imitate the behavior of the model under study


Introduction to Simulations

Simulation is the imitation of a real-world process or system over time [Banks et al.]

It is used for analysis and study of complex systems

Simulation requires the development of a simulation model

Computer-based experiments are conducted to describe, explain, and predict the behaviour of the real system


Advantages of Simulations

Effects of variations in the system parameters can be observed without disturbing the real system

New system designs can be tested without committing resources for their acquisition

Hypotheses on how or why certain phenomena occur can be tested for feasibility

Time can be expanded or compressed to allow for speed up or slow down of the phenomenon under investigation

Insights can be obtained about the interactions of variables and their importance

Bottleneck analysis can be performed in order to discover where work processes are being delayed excessively


Disadvantages of Simulations

Model building requires special training

Simulation results are often difficult to interpret. Most simulation outputs are random variables - based on random inputs – so it can be hard to distinguish whether an observation is the result of system inter-relationship or randomness

Simulation modeling and analysis can be time consuming and expensive


The problem can be solved by common sense

The problem can be solved analytically

It is less expensive to perform direct experiments

Costs of modeling and simulation exceed savings

Resources or time are not available

Lack of necessary data

System is very complex or cannot be defined

When are Simulations not Necessary


Modifying System Models

Adopting Distributed/Parallel Processing

Utilizing customized simulation packages for the system under study

Looping around Simulation Limitations


Static Dynamic

Discrete Continuous

Classification of Simulation Models

Deterministic Stochastic


Static

• Monte Carlo Simulation Represents a system snapshot at a particular point in time

Dynamic

• Represents systems as they change over time

Static and Dynamic models


Deterministic• Contain no random

variables• Has a known set of

inputs that will result in a unique set of outputs

Stochastic• Has one or more

random variables• Random inputs lead to

random outputs• Random outputs only

estimates of the true characteristics of the system

Deterministic and Stochastic Models


Discrete

• Simulation progress over discrete time instants

Continuous

• Simulation progresses over continuous time

Discrete and Continuous Models

Modeling & Simulation: An Introduction Some slides in this presentation have been copyrighted to Dr....

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