system simulation and modelling course code: mca 52 faculty : sailaja kumar k

Introduction to Simulation K.Sailaja Kumar1

SYSTEM SIMULATION AND MODELLING

Course Code: MCA 52

Faculty : Sailaja Kumar k


What is this course about?(1/3)

Simulation is a technique to analyze and predict the behavior of existing or proposed systems by experimenting with representative models of the systems.

This course is primarily about imitating the operation of real-world systems using computer programs. Our focus will be on “discrete-event” simulations.



We will learn how to: Abstract real-world systems into models Implement models using software Experiment design

Systems modeling requires understanding of Basic probability, statistics, elementary

calculus



In practice simulation models are mostly built on computer systems. Several languages and software packages facilitate the model building and experimentation process.

The Unified Modeling Language (UML) will be used for modeling and documentation when appropriate.


Course Outline

Introduction to Simulation Simulation Examples General Principles & Queuing Models Generating Random-Numbers Generating Random-Variates Input Modelling Verification and Validation of Simulation

Models Output Analysis for a Single Model


Books Lecture material primarily drawn from:

Discrete-Event System Simulation (Third Edition), Banks, Carson, Nelson, and Nicol, Prentice-Hall, 2007.

References Simulation Modeling and Analysis. (Fourth

Edition), Averill M Law,W David Kelton, McGraw Hill

Discrete – Event Simulation: A First Course Lawrence M. Leemis, Stephen K. Park:

Pearson / Prentice-Hall, 2006.


Introduction to Modeling and Simulation What is simulation? Systems and system Environment Components of a system Discrete and continuous Systems Model of a system Types of models Discrete-Event System Simulation When Simulation is the appropriate Tool When Simulation is not appropriate Advantages and Disadvantages of Simulation Application areas of simulation Steps in a simulation study


What is a simulation?(1/2) Simulation – is imitation of the operation of a

real world process or system over a time period, usually using a computer

The behavior of a system over a time period is studied by developing a simulation model

Simulation modeling can be used As an analysis tool for predicting the effect of changes

to existing systems

As a design tool to predict the performance of new systems under varying sets of circumstances.


What is a simulation?(2/2)

A simple Simulation model can be developed by mathematical methods.

Many real world systems models are developed using numerical computer-based simulation methods.

The simulation-generated data is used to estimate the measures of performance of the system.


When simulation is the appropriate tool (1/3)

To study and experiment with the internal interactions of a complex system or subsystem To study the effect of informational, organizational and environmental changes on a system Knowledge gained in designing a simulation model may help to suggest improvements Changing inputs and observing resulting outputs reveals which variables are most important and how they interact As a pedagogical device to reinforce analytic solution methodologies To experiment with new designs or policies prior to implementation To verify analytic results


When simulation is the appropriate tool (2/3) Simulation can be used for the following purposes: Simulation enables the study of experiments with internal interactions Informational, organizational, and environmental changes can

be simulated to see the model’s behavior Knowledge from simulations can be used to improve the

system Observing results from simulation can give insight to which variables are the most important ones Simulation can be used as pedagogical device to reinforce the learning material Simulations can be used to verify analytical results, e.g. queueing systems Animation of a simulation can show the system in action, so that the plan can be visualized


When to use simulations?(3/3) Simulations can be used:

To study complex system, i.e., systems where analytic solutions are infeasible.

To compare design alternatives for a system that doesn’t exist.

To study the effect of alterations to an existing system. Why not change the system??

To reinforce/verify analytic solutions.


When simulation is not appropriate (1/2)Simulation should not be used, in the case when problem is solvable by common sense when the problem can be solved mathematically when direct experiments are easier when the simulation costs exceed the savings when the simulation requires time, which is not

available when no (input) data is available, but simulations

need data when the simulation cannot be verified or validated when the system behavior is too complex or

unknownExample: human behavior is extremely complex to

model


When simulation is not appropriate(2/2)Simulations should not be used:

If model assumptions are simple such that mathematical methods can be used to obtain exact answers (analytical solutions)


Advantages of simulation(1/3)

Policies, procedures, decision rules, information flows can be explored without disrupting the real system

New hardware designs, physical layouts, transportation systems can tested without committing resources

Hypotheses about how or why a phenomena occur can be tested for feasibility

Time can be compressed or expanded - Slow-down or Speed-up Insight can be obtained about the interaction of

variables



Insight can be obtained about the importance of variables to the performance of the system

Bottleneck analysis can be performed to detect excessive delays

Simulation can help to understand how the system operates rather than how people think the system operates

“What if” questions can be answered



Once a model is built, it can be used repeatedly Simulation data can be less costly to obtain than data from the real system Simulation methods can be easier to apply than analytical methods Simulation models be more general and require fewer assumptions than analytical models Sometimes simulation is the only way to derive a solution to a problem


Disadvantages of simulation

• Model building requires training, it is like an art. - Compare model building with programming. • Simulation results can be difficult to interpret - Most outputs are essentially random variables - Thus, not simple to decide whether output is randomness or system behavior • Simulation can be time consuming and

expensive - Skimping in time and resources could lead to useless/wrong results



The disadvantages are offset as follows • Simulation packages contain models that only

need input data • Simulation packages contain output-analysis

capabilities • Sophistication in computer technology

improves simulation times • For most of the real-world problems there are

no closed form solutions



1. Developing non-trivial simulation models may be costly

2. Simulation is sometimes used when analytic

techniques will suffice 3. It is possible to become over-confident

with the simulated results


Advantages, disadvantages, and pitfalls in a simulation study

Advantages Simulation allows great flexibility in modeling complex

systems, so simulation models can be highly valid Easy to compare alternatives Control experimental conditions Can study system with a very long time frame

Disadvantages Stochastic simulations produce only estimates – with

noise Simulation models can be expensive to develop Simulations usually produce large volumes of output –

need to summarize, statistically analyze appropriately Pitfalls

Failure to identify objectives clearly up front In appropriate level of detail (both ways) Inadequate design and analysis of simulation

experiments Inadequate education, training


Systems and System Environment System: A collection of objects that are

joined together in some regular interaction or interdependence toward some purpose E.g. A production system manufacturing

automobiles. Here the machines, component parts, and

workers operate jointly to produce a high quality vehicle.

System Environment: changes occurring outside the system but affecting the system.


Components of a SystemEntity: Is an object of interest in the system.

E.g. Banking System• Customers.

Attribute: It is a property of an entity

E.g. Checking balance in their account.

Activity: Represents a time period of specified

length.

E.g. Making deposits.


Components of a System

State : Is the collection of variables necessary to describe the system at any time, relative to the objectives of the study.

E.g. State variables for a Bank are• Number of busy tellers, • The number of customers waiting in line to

be served• and Arrival Time of next customer


Components of a System Event: It is an instantaneous occurrence that changes

the state of the system. E.g. the arrival of a new customer.

Endogenous: used to describe activities and events occurring within a system.E.g. the completion of service of a customer

Exogenous: used to describe activities and events occurring in the environment that affect the system.E.g. the arrival of a customer


How to study a system?


Model of a System(1/2)Model : It is defined as a representation of a

system for the purpose of studying the system.

It is a simplification of the system.

Model represents only those aspects of the system that affect the problem under investigation

Model should be sufficiently detailed to permit valid conclusions to be drawn about the real system.


Model of a System(2/2)

Model contains only those components that are relevant to the study

Different models of the same system are required for the purpose of investigation changes.

It is used to study a system to understand the relationships

between its components Predict how the system will operate under a

new policy.


System vs. Its Model

• Simplification• Abstraction• Assumptions

Real System Model


Model Classification

Continuous-time vs. discrete-time models

Continuous-event vs. discrete-event

models

Deterministic vs. probabilistic models

Static vs. dynamic models

Linear vs. non-linear models

Open vs. closed models


Physical model Prototype of a system for the purpose of study.

Mathematical Model: Uses symbolic notation and mathematical equations to

represent a system.

E.g. A Simulation Model

Simulation Models: Static vs. Dynamic

Deterministic vs. Stochastic

Discrete vs. Continuous


Model Classification

Physical (prototypes)

Analytical (mathematical) Computer (Monte Carlo

Simulation) Descriptive (performance analysis) Prescriptive (optimization)


Types of Simulation Models

Static/DynamicA static simulation model, sometimes called a Monte Carlo simulation,

represent a system at a particular point in time.

A dynamic simulation model represents a

system as it changes over time.



Deterministic/Stochastic Simulation models that contain no random variables are classified as deterministic

Deterministic models have a known set of inputs that will result in a unique set of outputs.

A stochastic simulation model has one or more random variables as inputs.



Deterministic models produce deterministic results

Stochastic or probabilistic models are subject to random effects Typically, they have one or more random inputs

(e.g., arrival of customers, service time etc.). Outputs from stochastic models are “estimates”

of the true characteristics of the system Need to repeat experiments number of times Need to have confidence in the results



Discrete/Continuous State variables change instantaneously at

separated points in time E.g Bank model: State changes occur only

when a customer arrives or departs

State variables change continuously as a function of timeE.g. Airplane flight: State variables like position, velocity change continuously



Continuos systems in which the changes are predominantly smooth in time

• Natural events (rain, change of climate etc.)• Mechanical systems• Electrical systems

Discrete systems in which the state variable(s) change only at a discrete set of points in time

• Banks• Manufacturing• Computer systems



Discrete systems: Is one in which the state variables change only at a discrete set of points in time.

E.g. Banking system

The number of customers changes only at discrete points in time



Continuous systems: Is one in which the state variables change continuously over a time.

E.g. The head of water behind a dam

The head of water behind the dam, changes for this continuous

system


Continuous and Discrete-event models

Distancetraveled by plane

Time

(a) Continuous-event (b) Discrete-event

Number of cust. in queue

Time


Types of Simulation Models Continuous simulation

– Typically, solve sets of differential equations numerically over time– May involve stochastic elements– Some specialized software available; some discrete-event simulation software will do continuous simulation as well

Combined discrete-continuous simulation– Continuous variables described by differential equations

– Discrete events can occur that affect the continuously- changing variables

– Some discrete-event simulation software will do combined discrete-continuous simulation as well


Types of Simulation Models Discrete-event simulation: a simulation

using a discrete-event (also called discrete-state) model of the system E.g., Widely used for studying computer

systems Continuous-event simulation: uses a

continuous-state models E.g., Widely used in chemical/pharmaceutical

studies Our focus will be on discrete-event

systems.


Discrete-event system simulation Discrete and continuous models are defined similarly. However, a discrete simulation model is not always used to model a discrete system, nor is a continuous model always

used to model a continuous system.

Discrete-Event System Simulation

Discrete-event system simulation is widely used and is the focus of this course.

Discrete-event system simulation is the modeling of the systems in which the state variables change only at a discrete set of points in time.


Discrete-event system simulationModeling of a system as it evolves over time by a representation where the state variables change instantaneously at separated points in time

More precisely, state can change at only a countable number of points in time

These points in time are when events occur

Event: Instantaneous occurrence that may change the

state of the systemSometimes get creative about what an “event” is … e.g., end of simulation, Make a decision about a system’s operation

Can in principle be done by hand, but usually done on computer


More on models Static and dynamic models

Static models – system state independent of time Dynamic models - system state change with time

Linear and non-linear models Linear models – output is a linear function of

input parameters Open and closed models

(a) Open Model (b) Closed Model


Areas of Application

Application areas of simulation • Manufacturing applications • Semiconductor manufacturing • Construction engineering and project management • Military applications • Logistics, supply chain and distribution

applications • Transportation models and traffic • Business process simulation • Health care • Call-center • Computers and Networks • Games • Human Systems


Steps in a simulation study

1. Problem formulation 2. Setting objectives of study 3. Model building 4. Data collection 5. Implementation 6. Verification – is the implementation bug-free? 7. Validation – is the model accurate? 8. Experimental design 9. Production runs & analysis 10. Evaluate if results are satisfactory 11. Report results


Steps in a Simulation Study

1. Problem formulation Clearly understand problem Reformulation of the problem

2. Setting of objectives and overall project plan Which questions should be answered? Is simulation appropriate? Costs?

3. Model conceptualization No general guide Modeling tools in research, e.g. UML

4. Data collection How to get data? Are random distributions appropriate?

5. Model translation Program


Steps in a Simulation Study

6. Verified? Does the program that, what the model describes?

7. Validated? Do the results match the reality? In cases with no real-world system, hard to validate

8. Experimental design Which alternatives should be run? Which paramters should be varied?

9. Production runs and analysis 10. More runs? 11. Documentation and reporting

Program documentation – how does the program work Progress documentation – chronology of the work

12. Implementation

system simulation and modelling course code: mca 52 faculty : sailaja kumar k

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