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The Workload in the M/G/1 Queue with Work Removal

Published online by Cambridge University Press:  27 July 2009

Richard J. Boucherie  and
Onno J. Boxma
Richard J. Boucherie
Affiliation:
Department of Econometrics, University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands
Onno J. Boxma
Affiliation:
CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands and Tilburg University, Faculty of Economics, P.O. Box 90153, 5000 LE Tilburg, The Netherlands
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Extract

We consider an M/G/1 queue with the special feature of additional negative customers, who arrive according to a Poisson process. Negative customers require no service, but at their arrival a stochastic amount of work is instantaneously removed from the system. We show that the workload distribution in this M/G/1 queue with negative customers equals the waiting time distribution in a GI/G/1 queue with ordinary customers only; the effect of the negative customers is incorporated in the new arrival process.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 2 , April 1996 , pp. 261 - 277
Copyright
Copyright © Cambridge University Press 1996

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