Simulation and Modeling - 732B. Tech. (IT)

SEMESTER - VIISEMESTER - VII

Part I

July - 2013

System Simulation

Introduction

Simulation is a very powerful and widely used computational science technique for the analysis and study of complex systems.

Simulation may be defined as a technique that imitates the operation of a real-world system as it evolves over time. This is normally done by developing a simulation model. A This is normally done by developing a simulation model. A simulation model usually takes the form of a set of assumptions about the operation of the system, expressed as mathematical or logical relations between the objects of interest in the system.

Simulation has its advantages and disadvantages. We will focus our attention on simulation models and the simulation technique.

Simulation

What is simulation:

The process of designing a mathematical or

logical model of a real-system and then logical model of a real-system and then

conducting computer-based experiments with

the model to describe, explain, and predict

the behavior of the real system.

Simulation

Where simulation fits in

ProgrammingSimulation

Analysis

ModelingProbability &Statistics

Basic Terminology

In most simulation studies, we are concerned with

the simulation of some system.

Thus, in order to model a system, we must

understand the concept of a system.

Definition: A system is a collection of entities that

act and interact towards the accomplishment of

some logical end.

Systems generally tend to be dynamic their status

changes over time. To describe this status, we use

the concept of the state of a system.

Examples of - Simulation Model

Nano cars - numbers of cars produced per day

(throughput)

Emergency Room (beds, doctors, nurses), (minor,

moderate, major, critical)moderate, major, critical)

Missile Ballistic Missile Survivability against Some

Threat

Institutes (IIIT A) Parking place

Power Integration Semiconductor Capacity, and

random machine down times

Value of Simulation

Empirical Method verses Mathematical model

Allow you to calculate the extreme values not Allow you to calculate the extreme values not

just the expected value

Simulation

What is simulation

Simulation is the actual running of the model system to gain insight into its performance.system to gain insight into its performance.

Simulation

Why use simulation

Simulation is used to better understand the expected performance of the real system and to expected performance of the real system and to test the effectiveness of the system design.

Simulation

Why use simulation

Without building them

experimental system

new concepts new concepts

Without disturbing them

costly experimentation

unsafe experimentation.

Without destroying them

Determine limits of stress

Alternative to simulation

Simulation

Analytic models

Physical experimentation Physical experimentation

Visit other sites

Simulation vs. Analytic modeling

Advantage:

various performance measures

greater realism

easier to understand easier to understand

model the steady-state as well as the transit

behavior.

Disadvantage:

May not provide you with the optimal

solution

time to construct model will be longer.

Simulation vs. Physical

Advantage:

High Speed

Not disruptive

Replication easy Replication easy

Control variations

Generally less costly

Disadvantage:

Realism

Validity

Simulation vs. Alternatives

V A S PRealism

V A

V A S PCost

Representing system

System:

a collection of mutually interacting objects

designed to accomplish a goal (machines

repair system) repair system)

Entities:

denotes an element/object within boundary

of system (machines, operators, repairman)

Entity work being performed on object

Resource performing the work

Representing system

Attribute:

Characteristic or property or an entity

(machine ID, Type of breakdown, time that

machine went down) machine went down)

Activity:

transforms the state of an object usually over

some time (repairman service time, machine

run time)

Representing system

State of the system:

Numeric values that contain all the

information necessary to describe the system

at any time.at any time.

Delays:

Processes that take a conditional length of

time in the system

Representing system

Events:

Change the state of the system(end of service

of machine,machine breaks down)

Queue:

it is set, used to model waiting

Ex. Elevator systems

Entities

Elevators, people

Sets

People waiting at each floor

Attributes

Elevators capacity, speed, destination,

current location of each elevator

People inter-arrival time at each floor,

destination of each people

Ex. Elevator systems

State of system:

# of people on each elevator

# of people in each floor

Activities Activities

Load/Unloading passenger

Travel to next floor (speed and distance)

Persons travel to elevator

Ex. Elevator systems

Delays:

Persons waiting for elevator

Events:

Elevator arrival

End unloading

End Loading

Person Arrival

Simulation types

Static vs. dynamic

Deterministic vs. stochastic

Continuous vs. discrete

Simulation model system model Simulation model system model

Static Simulation vs. Dynamic

Simulation

There are two types of simulation models,

static and dynamic.

Definition: A static simulation model is a

representation of a system at a particular representation of a system at a particular

point in time.

We usually refer to a static simulation as a

Monte Carlo simulation.

Static Simulation vs. Dynamic

Simulation

Definition: A dynamic simulation is a representation of a system as it evolves over time.

Within these two classifications, a Within these two classifications, a simulation may be deterministic or stochastic.

A deterministic simulation model is one that contains no random variables; a stochastic simulation model contains one or more random variables.

Discrete Event vs. Continuous

Event Simulation

Discrete event:

state of system changes only at discrete points

in time(events)

ex. Machine repair problem ex. Machine repair problem

Programming

Look at system only when events occur; time is

advanced from event to event.

Discrete Event vs. Continuous

Event Simulation

Continuous event:

state of system changes continuously over

time

Ex. Level of fluid in tank Ex. Level of fluid in tank

Programming:

Advances time in small intervals. Use differential

equations to represent flows.

An Example of a Discrete-Event

Simulation

To simulate a queuing system, we first have to describe it.

We assume arrivals are drawn from an infinite calling population.

There is unlimited waiting room capacity, and There is unlimited waiting room capacity, and customers will be serve in the order of their arrival (FCFS).

Arrivals occur one at a time in a random fashion.

All arrivals are eventually served with the distribution of service teams as shown in the book.

Service times are also assumed to be random. After service, all customers return to the calling population.

For this example, we use the following variables to define the state of the system: (1) the number of define the state of the system: (1) the number of customers in the system; (2) the status of the server that is, whether the server is busy or idle; and (3)the time of the next arrival.

An event is defined as a situation that causes the state of the system to change instantaneously.

Discrete Event Simulation

Event scheduling

Write modules that describe changes in the

state of the system at each event

Main program advances time Main program advances time

One subprogram for each event

General purpose programming language

Discrete Event Simulation

Process interaction

Write modules that describe the progress of

entities through the system

As entities move the systems changes state As entities move the systems changes state

Entities are held to represent activities and

delays

Promodel programming language

Event scheduling

Time is advanced from event to event

Future events list ordered list of

upcoming events

As events are scheduled, they are added to

the list

As events occur they are removed from list

Activities in event ( one / event type)

Event scheduling

List is required to keep track of entities in a

set

Statistics Two types

Sample statistics average of some values

(W)

W = (W1 +W2 + +Wn)/n = Total Wait / # of wait

Time average statistics time weighted (L)

L = (0(t1) + 1(t2-t1) + 2(t3-t2) + 1(t4-t3)) / t4

Activity scanning

Activity scanning

Time is modeled in fixed time increments to

check if activity occurred

Small time increments is inefficient Small time increments is inefficient

Large time increments may miss activity

describes the activities in which the entities in

the system engage.

Process Oriented

Process oriented:

Many simulation models include elements which occur in defined patterns

The logic associated with such a system or The logic associated with such a system or events can be generalized and defined by a single statement

A simulation language could then translate such statement into the appropriate sequence of events

describes the processes through which the entities in the system flow.

Process Oriented

Process oriented:

These statements, define a sequence of

events which are automatically executed by

the simulation language as the entities move the simulation language as the entities move

through the process

Create arrival entities every t time units

However, since we are normally restricted to a

set of standardized statement, provided by

the simulation language, our model flexibility

is not as great as with the event condition

Feature provided by a language

Conceptual framework(entities, attributes, resource, queues)

Maintenance of event list

Random variable generation Random variable generation

Animation

Debugging function

Output analysis

Input analysis

Report generation

The Simulation Modeling Steps

We now discuss the process for a complete simulation study and present a systematic approach of carrying out a simulation.

A simulation study normally consists of several distinct stages. distinct stages.

However, not all simulation studies consist of all these stages or follow the order stated here.

On the other hand, there may even be considerable overlap between some of these stages.

Aircraft Performance Modelan example of Deterministic Systems Modeling

Lift force (L) = Weight of aircraft (W)Engine Thrust (T) = Drag force (D)

Aircraft Performance Model..

Expressions for lift and drag forces

Aircraft Performance Model..

Rate of decrease of aircraft weight due to fuel consumption

An empirical relation for drag polar relating CL and CD

Now the collection model equations

Aircraft Performance Model..

OR

The air density ratio at an altitude

T =

Where = 9296 below 11 Km

The Engineering

Problem Solving

43

Process

Newtons 2nd law of Motion

The time rate change of momentum of a body is equal to the resulting force acting on it.

Formulated as F = m.aF = net force acting on the body m = mass of the object (kg) a 2

44

a = its acceleration (m/s2)

Some complex models may require more sophisticated mathematical techniques than simple algebra

Example, modeling of a falling parachutist:

FU = Force due to air resistance = -cv (c = drag coefficient)FD = Force due to gravity = mg

UD FFF +=

cvmgdvcvF

mgFFFF

m

Fdtdv

U

D

UD

=

=

=

+=

=

This is a first order ordinary differential equation.

We would like to solve for v (velocity).

It can not be solved using algebraic manipulation

Analytical Solution:

If the parachutist is initially at rest (v=0 at t=0),

using calculus dv/dt can be solved to give the result:mdt

=

vm

cgdtdv

=

using calculus dv/dt can be solved to give the result:

( )tmcec

gmtv )/(1)( =

Independent variableDependent

variable

Parameters

Forcing function

**here Analytical Solution

( )tmcec

gmtv )/(1)( =

t (sec.) V (m/s)0 0

If v(t) could not be solved analytically, then we need to use a numerical method to solve

g = 9.8 m/s2 c =12.5 kg/s m = 68.1 kg

46

0 02 16.404 27.778 41.1010 44.8712 47.49 53.39

)()()(

lim........)()(

1

1

01

1

i

ii

ii

tii

ii

tvm

cgtt

tvtv

t

v

dtdv

tt

tvtv

t

v

dtdv

=

=

=

+

+

+

+

c

This equation can be rearranged to yield

Numerical Solution

47

))](([)()( 11 iii tttvm

cgtvtv ii += ++yield

t = 2 sec

To minimize the error, use a smaller step size, tNo problem, if you use a computer!

t (sec.) V (m/s)0 02 19.604 32.008 44.8210 47.9712 49.96 53.39

t (sec.) V (m/s)0 0

2 19.60

4 32.00

8 44.82

t (sec.) V (m/s)0 0

2 16.40

4 27.77

8 41.10

m=68.1 kg c=12.5 kg/s g=9.8 m/s t = 2 sec

Analytical

t (sec.) V (m/s)0 0

2 17.06

4 28.67

8 41.95

t = 0.5 sec

t (sec.) V (m/s)0 0

2 16.41

4 27.83

8 41.13

t = 0.01 sec

Numerical solutionvs.

8 44.82

10 47.97

12 49.96

53.39

8 41.10

10 44.87

12 47.49

53.39

( )tmcec

gmtv )/(1)( = ttv

m

cgtvtv iii +=+ )]([)()( 1

8 41.95

10 45.60

12 48.09

53.39

8 41.13

10 44.90

12 47.51

53.39

CONCLUSION: If you want to minimize the error, use a smaller step size, t

Manual Simulation Example

Given the following arrival times for a single server system what will be the average number in the queue, average number in the system, average time in system, average time in queue, the number of completed jobs, number in the queue, number in completed jobs, number in the queue, number in the system, and server utilization at time 15 if the service time is 3 time units for each entity.

1, 3, 5, 9,13,15,17

Distributive Systems

50

Distributive Systems

The Message Passing ParadigmMessage passing is the most fundamental paradigm for distributed

applications.

A process sends a message, often representing a request.

The message is delivered to a receiver, which processes the message,

and possibly sending a message in response.

In turn, the reply may trigger a further request, which leads to a

subsequent reply, and so forth.

51

In turn, the reply may trigger a further request, which leads to a

subsequent reply, and so forth.

Process A Process B

a message

Message passing

The Message Passing Paradigm - 2

The basic operations required to support the basic message passing paradigm are send, and receive.

For connection-oriented communication, the operations connect and disconnect are also required.

With the abstraction provided by this model, the interconnected processes perform input and output to each other, in a manner similar to file I/O. The I/O operations encapsulate the details of network

52

to file I/O. The I/O operations encapsulate the details of network communication at the operating-system level.

The ClientThe ClientThe ClientThe Client----Server ParadigmServer ParadigmServer ParadigmServer ParadigmBest known paradigm for network applications -- the client-server

model assigns asymmetric roles to two collaborating processes.

One process, the server, plays the role of a service provider which

waits passively for the arrival of requests. The other, the client,

issues specific requests to the server and awaits its response.

53

.

.

.

service request

a server processa client process

a service

The Client-Server Paradigm, conceptual

Server host

Client host

The ClientThe ClientThe ClientThe Client----Server ParadigmServer ParadigmServer ParadigmServer Paradigm - 2

Simple in concept, the client-server model provides an efficient

abstraction for the delivery of services.

Operations required include those for a server process to listen for

and to accept requests, and for a client process to issue requests

and accept responses.

By assigning asymmetric roles to the two sides, event

54

By assigning asymmetric roles to the two sides, event

synchronization is simplified: the server process waits for requests,

and the client in turn waits for responses.

Many Internet services are client-server applications. These

services are often known by the protocol that the application

implements. Well known Internet services include HTTP, FTP, DNS,

finger, gopher, etc.

The Peer-to-Peer System Architecturehttp://www.peer-to-peerwg.org/whatis/index.html

In system architecture and networks, peer-to-peer is an architecture where computer resources and services are directly exchanged between computer systems.

These resources and services include the exchange of information, processing cycles, cache storage, and disk storage for files

55

storage for files

In such an architecture, computers that have traditionally been used solely as clients communicate directly among themselves and can act as both clients and servers, assuming whatever role is most efficient for the network.

The Peer-to-Peer Distributed Computing

Paradigm

In the peer-to-peer paradigm, the participating processes play equal

roles, with equivalent capabilities and responsibilities (hence the

term peer). Each participant may issue a request to another

participant and receive a response.

process 1

Distributed Software Systems 56

requestresponse

request

response

process 2

Peer-to-Peer distributed

computingWhereas the client-server paradigm is an ideal model for a

centralized network service, the peer-to-peer paradigm is more

appropriate for applications such as instant messaging, peer-to-peer

file transfers, video conferencing, and collaborative work. It is also

possible for an application to be based on both the client-server

model and the peer-to-peer model.

Distributed Software Systems 57

model and the peer-to-peer model.

A well-known example of a peer-to-peer file transfer service is

Napster.comNapster.comNapster.comNapster.com or similar sites which allow files (primarily audio files)

to be transmitted among computers on the Internet. It makes use of

a server for directory in addition to the peer-to-peer computing.

Distributed Software Systems 58

Peer-to-Peer distributed

computingThe peer-to-peer paradigm can be implemented with facilities using any tool

that provide message-passing, or with a higher-level tool such as one that supports the point-to-point model of the Message System paradigm.

For web applications, the web agent is a protocol promoted by the XNSORG (the XNS Public Trust Organization) for peer-to-peer interprocess communication

Project JXTA is a set of open, generalized peer-to-peer protocols that allow

Distributed Software Systems 59

Project JXTA is a set of open, generalized peer-to-peer protocols that allow any connected device (cell phone, to PDA, PC to server) on the network to communicate and collaborate. JXTA is short for Juxtapose, as in side by side. It is a recognition that peer to peer is juxtapose to client server or Web based computing -- what is considered today's traditional computing model.