A Functional Equation Arising in a Queue With a Gating Mechanism
- 1 January 1989
- journal article
- research article
- Published by Cambridge University Press (CUP) in Probability in the Engineering and Informational Sciences
- Vol. 3 (3) , 417-433
- https://doi.org/10.1017/s0269964800001285
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.Keywords
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