queue-network

# queue-network - CDA6530: Performance Models of Computers...

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CDA6530: Performance Models of Computers and Networks Chapter 7: Basic Queuing Networks

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2 Open Queuing Network Jobs arrive from external sources, circulate, and eventually depart
3 Closed Queuing Network Fixed population of K jobs circulate continuously and never leave Previous machine-repairman problem

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4 Feed-Forward QNs Consider two queue tandem system Q: how to model? System is a continuous-time Markov chain (CTMC) State (N 1 (t), N 2 (t)), assume to be stable π (i,j) =P(N 1 =i, N 2 =j) Draw the state transition diagram But what is the arrival process to the second queue?
5 Poisson in Poisson out Burke’s Theorem: Departure process of M/M/ 1 queue is Poisson with rate λ independent of arrival process. Poisson process addition, thinning Two independent Poisson arrival processes adding together is still a Poisson ( λ = λ 1 + λ 2 ) For a Poisson arrival process, if each customer lefts with prob. p, the remaining arrival process is still a Poisson ( λ = λ 1 · p) Why?

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6 State transition diagram: (N 1 , N 2 ), N i =0,1,2,
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## This note was uploaded on 01/14/2012 for the course CDA 6530 taught by Professor Zou during the Fall '11 term at University of Central Florida.

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queue-network - CDA6530: Performance Models of Computers...

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