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Stochastic bounds for heterogeneous-server queues with Erlang service times

Published online by Cambridge University Press:  14 July 2016

Oliver S. Yu
Oliver S. Yu*
Affiliation:
Stanford Research Institute
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Abstract

This paper establishes stochastic bounds for the phasal departure times of a heterogeneous-server queue with a recurrent input and Erlang service times. The multi-server queue is bounded by a simple GI/E/1 queue. When the shape parameters of the Erlang service-time distributions of different servers are the same, these relations yield two-sided bounds for customer waiting times and the queue length, which can in turn be used with known results for single-server queues to obtain characterizations of steady-state distributions and heavy-traffic approximations.

Keywords

QUEUESERVICE SYSTEMCONGESTION THEORYMULTI-SERVER QUEUEHETEROGENEOUS-SERVER QUEUEQUEUE WITH ERLANG SERVICE TIMESSTOCHASTIC ORDERING OF QUEUESSTOCHASTIC BOUNDING RELATIONS FOR QUEUESEXISTENCE THEOREMS FOR QUEUESLIMIT THEOREMS FOR QUEUESAPPROXIMATIONS FOR QUEUESQUEUES IN HEAVY TRAFFIC
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 4 , December 1974 , pp. 785 - 796
Copyright
Copyright © Applied Probability Trust 1974 

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Footnotes

Research partially supported at Stanford University by the Office of Naval Research, the National Science Foundation and Stanford Research Institute.

References

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