Probability in the Engineering and Informational Sciences

Research Article

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

Richard J. Boucheriea1*, Onno J. Boxmaa2 and Karl Sigmana3

a1 Department of Econometrics, University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands

a2 CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands, Tilburg University, Faculty of Economics, P.O. Box 90153, 5000 LE Tilburg, The Netherlands

a3 Department of Industrial Engineering and Operations Research, Columbia University, 500 West 120th Street, New York, New York, 10027-6699

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.

Footnotes

* Research made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences.