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A cyclic queueing network with dependent exponential service times

Published online by Cambridge University Press:  14 July 2016

Patricia A. Jacobs
Patricia A. Jacobs*
Affiliation:
Stanford University
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Abstract

A cyclic queueing network with two servers and a finite number of customers is studied. The service times for server 1 form an earma(1,1) process (exponential mixed autoregressive moving average process both of order 1) which is a sequence of positively correlated exponential random variables; the process in general is not Markovian. The service times for the other server are independent with a common exponential distribution. Limiting results for the number of customers in queue and the virtual waiting time at server 1 are obtained. Comparisons are made with the case of independent exponential service times for server 1.

Keywords

CYCLIC QUEUEDEPENDENT EXPONENTIAL SERVICE TIMESEARMA(1,1) SEQUENCEMULTIPROGRAMMED COMPUTER SYSTEMGENERAL STATE SPACE MARKOV CHAINS
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 3 , September 1978 , pp. 573 - 589
Copyright
Copyright © Applied Probability Trust 1978 

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