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

D. Perry, W. Stadje, S. Zacks

Research output: Contribution to journalArticlepeer-review


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 ± 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.

Original languageEnglish
Pages (from-to)119-132
Number of pages14
JournalAnnals of Operations Research
Issue number1-4
StatePublished - 2002


  • Boundary crossing
  • Busy period
  • Compound Poisson process
  • Cycle maximum
  • Deterministic service time
  • Queue with negative customers
  • Two-sided stopping time

ASJC Scopus subject areas

  • General Decision Sciences
  • Management Science and Operations Research


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