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

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  • D. Perry
  • W. Stadje
  • S. Zacks

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

Suggested Citation

  • D. Perry & W. Stadje & S. Zacks, 2002. "Boundary Crossing for the Difference of Two Ordinary or Compound Poisson Processes," Annals of Operations Research, Springer, vol. 113(1), pages 119-132, July.
    • Handle: RePEc:spr:annopr:v:113:y:2002:i:1:p:119-132:10.1023/a:1020957827834
    DOI: 10.1023/A:1020957827834
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    Cited by:

    1. Pierre-Olivier Goffard, 2019. "Fraud risk assessment within blockchain transactions," Working Papers hal-01716687, HAL.
    2. R. Lenin & S. Ramaswamy, 2015. "Performance analysis of wireless sensor networks using queuing networks," Annals of Operations Research, Springer, vol. 233(1), pages 237-261, October.
    3. Gapeev, Pavel V. & Stoev, Yavor I., 2017. "On the Laplace transforms of the first exit times in one-dimensional non-affine jump–diffusion models," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 152-162.

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