DynamicSimulation - time) at any time of the day...

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STOCHASTIC PROCESSES
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Simulation Types Static Simulation Dynamic Simulation Estimation of the mean of a random variable Expected Profit Estimation of a performance measure from a random process Average Queue Length Average Inventory Level Shortage Probability
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Stochastic Processes A stochastic process { X t , t T} is a sequence of random variables (when T is discrete, e.g. T={ 0, 1, 2, …}) a “random function” (when T is continuous, e.g. T=[0,∞)) Index set T often represents time X t is a discrete or a continuous random variable
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Examples Inventory level of cars at the beginning of each day (discrete state, discrete time) Queue length at any time (discrete state, continuous time) Water level in a dam at the beginning of each day (continuous state, discrete
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Unformatted text preview: time) at any time of the day (continuous state, continuous time) Queue length observed by arriving customers (index set denotes the customer index, not time!) Random Variable vs. Stochastic Process Sample Space Real Numbers ' X( ) X( ) Sample Space Index ' X t ( ) X t ( ) Sample Paths Simulation: A Stochastic Experiment Dynamic Simulation: A Sample Path Analysis Objective : Analyze a finite number of sample paths to determine an expected performance of a stochastic process over all sample paths (there may be infinite number of them) For ergodic systems, observing a single sample path to time infinity one can determine the steady state expected performance over all sample paths...
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DynamicSimulation - time) at any time of the day...

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