MODELING and SIMULATION Modeling and Simulation Terminologies

Components of a System

Types of Simulation and Models

Steps in Simulation Process

Advantages and Disadvantages of Simulation Simulation of a system is the operation of a certain model derived from realistic setups or events. Model

a representation of a system under test

amenable to manipulation which would be impossible, too expensive, or not practical

model operation can be studied, and from this, properties concerning the behavior of the actual system can be inferred SYSTEM a group of objects that are joined together in some regular interaction or interdependence towards the accomplishment of some purpose. static - a system that does not vary with time (e.g. location of a building)

dynamic - one that varies with time (e.g. evolution of man) Entity - object of interest in the system

Attribute - property of an entity

Activity - represents a time period of specified length

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

Event - instantaneous occurrence that may change the state of the system

Progress of the system -studied by following the changes in the state of the system INTRODUCTION TO COMPONENTS OF A SYSTEM: is the process of designing a model of a real system and conducting experiments with this model for the purpose either of understanding the behavior of the system or evaluating various strategies for the operation of the system. What is a model? a representation of an object, a system, or an idea in some form other than that of the entity itself

a description of a system intended to predict what happens if certain actions are taken

modeling is a way of thinking and reasoning about systems

TYPES of MODEL:

Physical, Mathematical and Process SIMULATION USES OF MODEL study system behavior in the design stage, before such system is built

communicate a system design

predict the performance of new system under varying sets of circumstances

answer "What if" questions about the real-world system ROLE OF A SIMULATOR A simulator is a computer program which mimics both:

the internal behavior of a real-world system

the input processes which drive or control the simulated system

The simulator output is a set of measurements concerning the observable reactions and performance of the system.

Measurements are only estimates of what the real-world measurements actually are/ would be When do we simulate? Appropriate:

gain knowledge about improvement of system

the system as yet does not exist

experimentation with the system is expensive, too time consuming, too dangerous or is inappropriate

Not appropriate:

problem can be solved by common sense

problem can be solved analytically

easier to perform direct experiments

cost exceeding savings

resource and time are not available Discrete vs. continuous systems DISCRETE SYSTEM state variable change only at discrete set of points in time CONTINUOUS SYSTEM state variable changes continuously over time Model of Taxonomy and Alternatives input variables are random thus producing random outputs

several runs must be made to get an accurate performance estimate no randomness, all future states are determined once the input data and initial state have been defined.

have constant inputs and produce constant outputs.

will always produce the exact same outcome no matter how many times it is run Types of Simulation Models Monte Carlo Simulation - described system is both stochastic and static

Continuous Simulation - used to model systems that vary continually with time; system modeled are dynamic but may be either deterministic or stochastic

Discrete-Event Simulation - used to model systems that are assumed to change only at discrete set of points in time (corresponding to state changes); system modeled are dynamic and almost invariably stochastic

Combined Discrete/Continuous Simulation (Hybrid) Considerations The choice of simulation should be based on the following:

function of the system

characteristics of the system

objectives of the study STEPS IN DEVELOPING A DISCRETE-EVENT MODEL determine the goals and objective

build a conceptual model

convert into a specification model

convert into a computational model

verify and validate

iterate if necessary MODEL LEVELS Conceptual very high level, usually theoretical concepts discussion

what are the state variables, which are dynamic, and which are important?

How comprehensive should the model be? MODEL LEVELS Specification on paper

may involve equations, pseudocode

How will the model receive input? MODEL LEVELS Computational a computer program

general-purpose programming languages or simulation languages are used

actual implementation of simulation Steps in Simulation 1. Problem formulation

2. Setting objectives and overall project plan

3. Model conceptualization

4. Data collection

5. Model translation

6. Verified?

7. Validated?

8. Experimental design

9. Production runs and analysis

10. More runs

11. Documentation and reporting

12. Implementation Example: Simulation of a Queuing System Setup of a queuing system Calling population (finite, infinite) - customers. This can be adults, babies, pets and so on...

Nature of arrival - arrival times. Fast arrival times mean that the queue will be full at a faster rate.

Pattern of service - service time. This depends on the employee providing the service and the kind of transaction to be made.

System capacity - total customers that can be served at a given time.

Queuing discipline: FIFO, LIFO, etc.

State of system: number of customers in the queue, server (idle, busy)

An event cause an instantaneous change in system state

arrival of a customer (arrival event)

completion of service (departure event) ARRIVAL EVENT DEPARTURE EVENT EVENTS occur at random (initiates real life)

time to mark the occurrence of events are usually randomly generated

inter-arrival (or arrival) times and service times are determined (generated) from the distributions of these random variables Example: Simulation of Queuing System % server is idle = total idle time / total simulation time

average waiting time = total waiting time / number of customers Advantages of Simulation time can be compressed or expanded to allow for speedup or slow-down of the phenomenon

operating performance of new hardware designs, physical layouts, etc. can be tested prior to full-scale implementation

new policies, operating procedures, information flow, etc. can be explored without disrupting ongoing operation for the real system

answer "what if" question DISAdvantages of Simulation model building requires special training

simulation modeling, execution, and analysis can be time consuming and expensive

hidden critical assumption may cause the model to diverge from reality

model parameters may be difficult to initialize

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# Introduction to Modeling and Simulation

MODESIM - Week 1

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