Boundary Crossing for the Difference of Two Ordinary or Compound Poisson Processes

D. Perry, W. Stadje and S. Zacks

Annals of Operations Research, 2002, vol. 113, issue 1, 119-132

Abstract: We consider the lower boundary crossing problem for the difference of two independent compound Poisson processes. This problem arises in the busy period analysis of single-server queueing models with work removals. The Laplace transform of the crossing time is derived as the unique solution of an integral equation and is shown to be given by a Neumann series. In the case of ±1 jumps, corresponding to queues with deterministic service times and work removals, we obtain explicit results and an approximation useful for numerical purposes. We also treat upper boundaries and two-sided stopping times, which allows to derive the conditional distribution of the maximum workload up to time t, given the busy period is longer than t. Copyright Kluwer Academic Publishers 2002

Keywords: compound Poisson process; boundary crossing; queue with negative customers; busy period; deterministic service time; two-sided stopping time; cycle maximum (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1023/A:1020957827834

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