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A Note on Negative Customers, GI/G/1 Workload, and Risk Processes

Published online by Cambridge University Press:  27 July 2009

Richard J. Boucherie ,
Onno J. Boxma  and
Karl Sigman
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, Tilburg University, Faculty of Economics, P.O. Box 90153, 5000 LE Tilburg, The Netherlands
Karl Sigman
Affiliation:
Department of Industrial Engineering and Operations Research, Columbia University, 500 West 120th Street, New York, New York, 10027-6699
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Abstract

This note illustrates that a combination of the approach in our previous papers (Boucherie and Boxma, 1996, Probability in the Engineering and Informational Sciences10: 261–277; Jain and Sigman, 1996, Probability in the Engineering and Informational Sciences 10: 519–531) directly leads to a Pollaczek-Khintchine form for the workload in a queue with negative customers. The same technique is also applied to risk processes with lump additions.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 3 , July 1997 , pp. 305 - 311
Copyright
Copyright © Cambridge University Press 1997

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