Lecture_1_Notes

# Lecture_1_Notes - Introduction to Discrete Event Simulation...

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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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Lecture_1_Notes - Introduction to Discrete Event Simulation...

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