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

  • Richard J. Boucherie (a1), Onno J. Boxma (a2) and Karl Sigman (a3)

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.

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1.Asmussen, S. & Sigman, K. (1996). Monotone stochastic recursions and their duals. Probability in the Engineering and Information Sciences 10: 120.
2.Boucherie, R.J. & Boxma, O.J. (1996). The workload in the M/G/l queue with work removal. Probability in the Engineering and Informational Sciences 10: 261277.
3.Cohen, J.W. (1982). The single server queue. Amsterdam: North-Holland.
4.Cramér, H. (1955). Collective risk theory. Reprinted from the Jubilee Volume of Skandia Insurance Company, Esselte, Stockholm.
5.Fakinos, D. (1981). The G/G/l queueing system with a particular queue discipline. Journal of the Royal Statistical Society B 43: 190196.
6.Gelenbe, E. (1991). Product-form queueing networks with negative and positive customers. Journal of Applied Probability 28: 656663.
7.Gelenbe, E. (1993). G-networks with triggered customer movement. Journal of Applied Probability 30: 742748.
8.Jain, G. & Sigman, K. (1996). Generalizing the Pollaczek-Khintchine formula to account for arbitrary work removal. Probability in the Engineering and Informational Sciences 10: 519531.
9.Jain, G. & Sigman, K. (1996). A Pollaczek-Khintchine formulation for M/G/l queues with disasters. Journal of Applied Probability 33: 11911200.
10.Lukacs, E. (1970). Characteristic functions. London: Charles Griffin.
11.Niu, S.-C. (1988). Representing workloads in GI/G/1 queues through the preemptive-resume L1FO queue discipline. Queueing Systems 3: 157178.
12.Prabhu, N.U. (1961). On the ruin problem of collective risk theory. Annals of Mathematical Statistics 32: 757764.
13.Siegmund, D. (1976). The equivalence of absorbing and reflecting barrier problems for stochastically monotone Markov processes. Annals of Probability 4: 914924.
14.Sigman, K. (1996). Continuous time stochastic recursions and duality. Manuscript.
15.Wolff, R.W. (1989). Stochastic modeling and the theory of queues. Englewood Cliffs, New Jersey: Prentice-Hall.

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

  • Richard J. Boucherie (a1), Onno J. Boxma (a2) and Karl Sigman (a3)

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