11. Stoch (OR Models)

# 11. Stoch (OR Models) - Lecture11Stochastic Processes...

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Lecture 11 – Stochastic  Processes Topics • Definitions • Review of probability • Realization of a stochastic process • Continuous vs. discrete systems • Examples

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Basic Definitions Stochastic process :  System that changes over time in an uncertain  manner Examples Automated teller machine (ATM) Printed circuit board assembly operation Runway activity at airport State : Snapshot of the system at some fixed point in time Transition : Movement from one state to another
Elements of Probability Theory Experiment : Any situation where the outcome is uncertain. Sample Space , S : All possible outcomes of an experiment (we will call them the “state space”). Event : Any collection of outcomes (points) in the sample space. A collection of events E 1 , E 2 ,…, E n is said to be mutually exclusive if E i E j = for all i j = 1,…, n. Random Variable (RV) : Function or procedure that assigns a real number to each outcome in the sample space. Cumulative Distribution Function (CDF) , F (·): Probability distribution function for the random variable X such that F ( a ) Pr{ X a }

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Components of Stochastic Model Time : Either continuous or discrete parameter. t 1 t 2 t 3 t 0 t 4 t im e State : Describes the attributes of a system at some point in time. s = ( s 1 , s 2 , . . . , s v ); for ATM example s = ( n ) Convenient to assign a unique nonnegative integer index to each possible value of the state vector. We call this X and require that for each s X .
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## This note was uploaded on 12/19/2011 for the course M E 366l taught by Professor Staff during the Spring '08 term at University of Texas.

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11. Stoch (OR Models) - Lecture11Stochastic Processes...

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