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Customers arrive to a single server system according to a Poisson process with rate λ. An arrival that finds the server idle immediately begins service; an arrival that finds the server busy waits. When the server completes a service it then simultaneously serves all those customers who are waiting. The time it takes to serve a group of size i is a random variable with density function gi, i≥ 1. If X, is the number of customers in the nth service batch, is {Xn, n ≥ 0} a Markov chain. If it is, give its transition probabilities; if it is not, tell why not.

Customers arrive to a single server system according to a Poisson process with rate λ. An arrival that finds the server idle immediately begins service; an arrival that finds the server busy waits. When the server completes a service it then simultaneously serves all those customers who are waiting. The time it takes to serve a group of size i is a random variable with density function gi, i≥ 1. If X, is the number of customers in the nth service batch, is {Xn, n ≥ 0} a Markov chain. If it is, give its transition probabilities; if it is not, tell why not.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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Customers arrive to a single server system according to a Poisson process with rate .. An arrival that finds the server idle immediately begins service; an arrival that finds the server busy waits. When the server completes a service it then simultaneously serves all those customers who are waiting. The time it takes to serve a group of size i is a random variable with density function gi, i> 1. If X, is the number of customers in the nth service batch, is {Xn, n > 0} a Markov chain. If it is, give its transition probabilities; if it is not, tell why not.
Transcribed Image Text:Customers arrive to a single server system according to a Poisson process with rate .. An arrival that finds the server idle immediately begins service; an arrival that finds the server busy waits. When the server completes a service it then simultaneously serves all those customers who are waiting. The time it takes to serve a group of size i is a random variable with density function gi, i> 1. If X, is the number of customers in the nth service batch, is {Xn, n > 0} a Markov chain. If it is, give its transition probabilities; if it is not, tell why not.
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