Boundary crossing for the difference of two ordinary or compound Poisson processes

Boundary crossing for the difference of two ordinary or compound Poisson processes

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Article ID: iaor20032092
Country: Netherlands
Volume: 113
Issue: 1
Start Page Number: 119
End Page Number: 132
Publication Date: Jul 2002
Journal: Annals of Operations Research
Authors: , ,
Keywords: markov processes
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.

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