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Unformatted text preview: Introduction to Discrete Event Simulation The System The system is some sort of facility or process that we want to learn more about and understand, and study in a scientific fashion. Example : Customers entering a bank, being served by a teller and leaving. A Model A model is a set of assumptions and mathematical and logical relationships used to characterize the system in a conceptual way that makes it easier to study the system. Example: An M/M/k queueing model Aside: M/M/k A system where the time between customer arrival are Exponentially distributed. Customers wait FIFO in line until one of k servers becomes available. Their service time is also Exponentially distributed. Once service is complete, customers leave. (M stands for Markovian). A Simulation A simulation is a model that behaves like the real system Examples : Flight training simulators for pilots Pilot plants for chemical processes Wind tunnels Solid models Computer models of car crashes Climate models A simulation does not behave exactly like the real system. It behaves like part of the real system. Purpose Each simulation model (indeed any model) must be built with a purpose (i.e. to answer specific questions). * This is important ! This is how we know what parts of the real system should be included in the simulation model. Why Simulation? Analytic models are too complex To experiment with the system. We can simulate without having to: Build the real system Pay for the operation of the real system Wait for the system to operate in real time Model all trivial aspects of the system Risk catastrophic failures That is, it is EASIER, CHEAPER and FASTER than experimenting with the real system What is Discrete Event Simulation? A means by which certain systems can be simulated What kind of systems? Discrete Event Dynamic Systems Systems with some or all of the following features: Components of a DEDS System The system operates over time: it is a process . Randomness is involved. Scarce resources Entities which flow through the system requiring resources in order to perform activities . Waiting lines ( queues ) where the entities wait for needed resources to become available. Priority rules for the flow of entities and the use of resources . How do we handle the random stuff? Monte Carlo Simulation Monte Carlo Simulation Monte Carlo simulation is used to discover the behavior of functions of random variables . Usually very complex functions. Typical situation in simple Monte Carlo studies: Given random variables X 1 , X 2 , . , X N with known distributions f (x 1 ), f (x 2 ), ., f (x N ) or rather with known joint distribution f(X 1 , X 2 , . , X N ) Let Y = H(X 1 , X 2 , . , X N ) where H is some (possibly very complex) function What can we say about the distribution of Y?...
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 Spring '08
 Storer

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