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Queues with negative arrivals

Published online by Cambridge University Press:  14 July 2016

Erol Gelenbe ,
Peter Glynn  and
Karl Sigman
Erol Gelenbe*
Affiliation:
University René Descartes
Peter Glynn*
Affiliation:
Stanford University
Karl Sigman*
Affiliation:
Columbia University
*
∗Postal address: Ecole des Hautes Etudes en Informatique, Université René Descartes (Paris V), 45 rue des Saints-Peres, 45006 Paris, France.
∗∗Postal address: Department of Operations Research, Stanford University, Stanford, CA 943054022, USA.
∗∗∗Postal address: Department of Industrial Engineering and Operations Research, Columbia University, New York NY 10027, USA.
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Abstract

We study single-server queueing models where in addition to regular arriving customers, there are negative arrivals. A negative arrival has the effect of removing a customer from the queue. The way in which this removal is specified gives rise to several different models. Unlike the standard FIFO GI/GI/1 model, the stability conditions for these new models may depend upon more than just the arrival and service rates; the entire distributions of interarrival and service times may be involved.

Keywords

STABILITYREMOVALS
Type
Short Communications
Information
Journal of Applied Probability , Volume 28 , Issue 1 , March 1991 , pp. 245 - 250
Copyright
Copyright © Applied Probability Trust 1991 

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Footnotes

Research supported in part by CNRS-CS (French National Program on Parallel Computation).

Research supported by the U.S. Army Research Office under Contract DAAL-03-88-K-0063.

Research supported by NSF Grant DDM 895–7825.

References

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