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A Functional Equation Arising in a Queue With a Gating Mechanism

Published online by Cambridge University Press:  27 July 2009

David L. Jagerman  and
Bhaskar Sengupta
David L. Jagerman
Affiliation:
AT/T Bell Laboratories Holmdel New Jersey 07733
Bhaskar Sengupta
Affiliation:
AT/T Bell Laboratories Holmdel New Jersey 07733
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Abstract

Our primary aim in this paper is to study a functional equation that arises in a problem of queueing. Consider a queue with compound Poisson arrivals and general service times with a gating mechanism. The gating mechanism takes in at most m(≤∞) customers at a time for service and serves these customers according to the processor-sharing discipline. In this paper, we examine various performance characteristics for this queue. The characteristics include waiting-time distribution, queue-length distribution, time spent with the server, and batch-size distribution for service.

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Type
Articles
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Probability in the Engineering and Informational Sciences , Volume 3 , Issue 3 , July 1989 , pp. 417 - 433
Copyright
Copyright © Cambridge University Press 1989

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