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Limiting diffusion approximations for the many server queue and the repairman problem

Published online by Cambridge University Press:  14 July 2016

Donald L. Iglehart
Donald L. Iglehart*
Affiliation:
Cornell University
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Extract

We shall consider a many server (multiple channels in parallel) queueing process in which customers arrive at the queue according to a Poisson process. The service times are assumed to be independent and exponentially distributed. As usual, the service times are independent of the arrival process. We assume that no server is idle if there is a customer waiting, but that otherwise the service discipline is arbitrary. If there are n servers and we let Xn(t) denote the number of customers waiting or being served at time t, then it is well known that Xn(t) is a birth and death process with stationary transition probabilities. A very comprehensive analysis of this many server queue from the point of view of birth and death processes has been carried out by Karlin and McGregor [5].

Type
Research Papers
Information
Journal of Applied Probability , Volume 2 , Issue 2 , December 1965 , pp. 429 - 441
Copyright
Copyright © Applied Probability Trust 

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