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## Stochastic Processes

by: Mafalda Ebert

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# Stochastic Processes OR 645

Mafalda Ebert
Mason
GPA 3.9

John Shortle

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COURSE
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John Shortle
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PAGES
1
WORDS
KARMA
50 ?

## Popular in Operations And Info Mgmt

This 1 page Study Guide was uploaded by Mafalda Ebert on Monday September 28, 2015. The Study Guide belongs to OR 645 at George Mason University taught by John Shortle in Fall. Since its upload, it has received 40 views. For similar materials see /class/215267/or-645-george-mason-university in Operations And Info Mgmt at George Mason University.

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Date Created: 09/28/15
OR 645 Stochastic Models 11 Lecture 8 Exam Review Renewal Theory Given 112 2004 Renewal Theory Generalization of the Poisson Process wherein you allow any distribution for an arrival rate Example X1 r H V V v v Time arrivals DEFN X is the time between n1st and nm arrivals Let s saythati 30 minutes and there is variation Question if you show up for the Metro how long do you wait Intu on says the average wait would bay 2 minutes Answer Var G E G Var G EWg g 2 2EG 2 2EG Example 1 Let G N Deterministic with length 1 Example 2 Let G N exp1u DEFN t2 0 a counting process is a renewal process if Xquot are iid N G Nl is the number of arrivals at time t DEFN Let n Sn 2X n 2 1 time nm event occurred Notation Fdenotes interarrival distribution 11 Assume F0 lt I CDF Probability of the interarrival times being 0 zero So we are saying that interarrival times are gt 0 F0 0 gt two or more arrivals cannot occur at the same time F0 gt 0 gt two or more arrivals can occur at the same time Notation u EXn where U is a mean not a rate Notation N0 2 n ltgt Sn f t DEFN mt expected number of vtL i r ti i39iH Fora Lecture by John Shortle transcribed by James LaBeIIe based on the class textbook Ross 8 M 2003 Introduction to Probability Modes 8m Academic Press

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