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The interchangeability of tandem queues with heterogeneous customers and dependent service times

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Richard R. Weber
Richard R. Weber*
Affiliation:
University of Cambridge
*
∗Postal address: University Engineering Department, Management Studies Group, Mill Lane, Cambridge CB2 1RX, UK.
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Abstract

Consider m queueing stations in tandem, with infinite buffers between stations, all initially empty, and an arbitrary arrival process at the first station. The service time of customer j at station i is geometrically distributed with parameter pi, but this is conditioned on the fact that the sum of the m service times for customer j is cj. Service times of distinct customers are independent. We show that for any arrival process to the first station the departure process from the last station is statistically unaltered by interchanging any of the pi's. This remains true for two stations in tandem even if there is only a buffer of finite size between them. The well-known interchangeability of ·/M/1 queues is a special case of this result. Other special cases provide interesting new results.

Keywords

OUTPUT PROCESSES

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Research Article
Information
Advances in Applied Probability , Volume 24 , Issue 3 , September 1992 , pp. 727 - 737
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

This research has been supported in part by NSF Grant DDM-8914863.

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