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Rare events in series of queues

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Pantelis Tsoucas
Pantelis Tsoucas*
Affiliation:
IBM Research Division
*
∗ Postal address: IBM Research Division, T. J. Watson Research Center, P.O. Box 704, Yorktown Heights, NY 10598, USA.
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Abstract

In an ergodic network of K M/M/1 queues in series we consider the rare event that, as N increases, the total population in the network exceeds N during a busy period. By utilizing the contraction principle of large deviation theory, an action functional is obtained for this exit problem. The ensuing minimization is carried out for K = 2 and an indication is given for arbitrary K. It is shown that, asymptotically and for unequal service rates, the ‘most likely' path for this rare event is one where the arrival rate has been interchanged with the smallest service rate. The problem has been posed in Parekh and Walrand [7] in connection with importance sampling simulation methods for queueing networks. Its solution has previously been obtained only heuristically.

Keywords

LARGE DEVIATIONSQUEUES IN SERIES

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 1 , March 1992 , pp. 168 - 175
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

A version of this work was presented at the ORSA/TIMS Conference, New York, NY, 16–18 October 1989.

References

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