Modeling and Simulation An Introduction 1 The Nature

Modeling and Simulation (An Introduction) 1

The Nature of Simulation �Conceptions �Application areas �Impediments 2

Conceptions �Simulation course is about techniques for using computers to imitate or simulate the operations of various kinds of real world facilities or processes. �A simulation is the imitation of the operation of a real-world process or system over time. Steps include �Generating an artificial history of a system �Observing the behavior of that artificial history �Drawing inferences concerning the operating characteristics of the real system 3

Conceptions �Use the operation of a bank as an example: �Counting how many people come to the bank; how many tellers, how long each customer is in service; etc. �Establishing a model and its corresponding computer program. �Executing the program, varying parameters (number of tellers, service time, arrival intervals) and observing the behavior of the system. �Drawing conclusions: increasing number of tellers; reducing service time; changing queuing strategies; etc. 4

Conceptions �The behavior of a system as it evolves over time is studied by developing a simulation model. �A model is a set of entities and the relationship among them. For the bank example: entities would include customers, tellers, and queues. Relations would include customers entering a queue; tellers serving the customer; customers leaving the bank. �Once developed, a model has to be validated. There are many different ways to validate a model: observation (measurement); analytical model comparison (analysis). 5

Application areas �Designing and analyzing manufacturing systems �evaluating military weapons systems or their logistics requirements �determining hardware requirements or protocols for communication networks �Determining hardware and software requirements for a computer system �Designing and operating transportation systems such as airports, freeways, ports and subways 6

Application areas �Evaluating designs for service organizations such as call centers, fast-food restaurants, hospitals, and post offices. �Reengineering of business processes �Determining ordering polices for an inventory system �Analyzing financial or economic systems. 7

Impediments § Models used to study large-scale systems tend to be very complex, and writing computer programs to execute them can be an arduous task indeed. (excellent software products) § Large amount of computer time is sometimes required. (cheaper and faster computer) § An unfortunate impression that simulation is just an exercise in computer programming, albeit a complicated one. (attitude, simulation methodology) 8

Systems, Models & Simulation �System is defined to be a collection of entities, e. g. , people or machines, which act and interact together toward the accomplishment of some logical end. �System depends on the objectives of a particular study. �State of a system: collection of variables necessary to describe a system at a particular time, relative to the objectives of a study. (the number of busy tellers, the number of customers in the bank, the time of arrival of each customer in the bank) �Types of systems: Discrete and continuous. 9

Continue. . . Ø discrete system: the state variables change instantaneously at separated points in time. (a bank, e. g. , the number of customers in the bank) Ø continuous system: the state variables change continuously with respect to time. (an airplane moving through the air, e. g. , position and velocity ) • Many systems are partly discrete, partly continuous �Study on a system: try to gain some insight into the relationships among various components, or to predict performance under some new conditions being considered. �Ways to study a system: 10

Example · One study on a bank to determine the number of tellers needed to provide adequate service for customers who want just to cash a check or make a savings deposite, the system can be defined to be that portion of the bank consisting of the tellers and the customers waiting in line or being served. · If the loan officer and the safety deposite boxes are to be included, the definition of the system must be expanded in an obvious way. 12

Systems, Models & Simulation • Classification of simulation models – Static vs. dynamic – Deterministic vs. stochastic – Continuous vs. discrete • Most operational models are dynamic, stochastic, and discrete – will be called discrete-event simulation models 13

Types of Simulation

Model Classifications � deterministic (input and output variables are fixed); � stochastic (at least one of the input or output variables is probabilistic); � static (time is not taken into account); � dynamic (time-varying interactions among variables are taken into account). 15

System Terminology: � State: � A variable characterizing an attribute in the system such as level of stock in inventory or number of jobs waiting for processing �Event: � An occurrence at a point in time which may change the state of the system, such as arrival of a customer or start of work on a job. 16

System Terminology: � Entity: � An object that passes through the system, such as cars in an intersection or orders in a factory. Often an event (e. g. , arrival) is associated with an entity (e. g. , customer). �Queue: � A queue is not only a physical queue of people, it can also be a task list, a buffer of finished goods waiting for transportation or any place where entities are waiting for something to happen for any reason. 17

System Terminology: � Creating is causing an arrival of a new entity to the system at some point in time. �Scheduling: � Scheduling is the act of assigning a new future event to an existing entity. 18

System Terminology: � Random Variable: � is a quantity that is uncertain, such as interarrival time between two incoming flights or number of defective parts in a shipment. �Random Variate: � is an artificially generated random variable. 19

System Terminology: � Distribution: � is the mathematical law which governs the probabilistic features of a random variable. 20

Example: � Building a simulation gas station with a single pump served by a single service man � assume that the arrival of cars as well as their service times are random 21

Solution (1): � At first identify the: states � events � entities � queue � random realizations � distributions � 22

Solution (1): �after identification of the different system requirements, you will come up with the different values: � states: o Number of cars waiting for service, number of cars served at any moment � events: o Number of cars, start of service, end of service � entities: o cars 23

Solution (1): � queue o The queue of cars in front of the pump, waiting for services � random realizations: o inter-arrival times, service times � distributions: o assume exponential distribution for both inter- arrival time and service time 24

Solution (2): Arrival Routine 25

Solution (2): Departure Routine 26