Modeling and Simulation (An Introduction)

The Nature of Simulation Conceptions Application areas Impediments

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

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.

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).

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

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.

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)

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.

Continue... Many systems are partly discrete, partly continuous discrete system: the state variables change instantaneously at separated points in time. (a bank, e.g., the number of customers in the bank) 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:

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.

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

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).

System Terminology: State: Event: 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.

System Terminology: Entity: Queue: 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.

System Terminology: Creating: Scheduling: 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.

System Terminology: Random Variable: Random Variate: 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.

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

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

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

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

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

Solution (2): Arrival Routine

Solution (2): Departure Routine