Boundary Crossing for the Difference of Two Ordinary or Compound Poisson Processes |
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Authors: | D Perry W Stadje S Zacks |
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Institution: | (1) Department of Statistics, University of Haifa, 31905 Haifa, Israel;(2) Fachbereich Mathematik/Informatik, University of Osnabrück, 49069 Osnabrück, Germany;(3) Department of Mathematical Sciences, Binghamton University, Binghamton, NY 13902-6000, USA |
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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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Keywords: | compound Poisson process boundary crossing queue with negative customers busy period deterministic service time two-sided stopping time cycle maximum |
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