Hitting and ruin probabilities for compound Poisson processes and the cycle maximum of the M/G/1 queue

D. Perry, W. Stadje, S. Zacks

Research output: Contribution to journalArticlepeer-review

Abstract

We derive a new formula for the probability that a compound Poisson process with positive jumps hits a lower straight line before it crosses a parallel upper line. This yields a new approach to determine the distribution of the cycle maximum of the M/G/1 queue. Moreover, we express the hitting probabilities in terms of the corresponding ruin probabilities.

Original languageEnglish
Pages (from-to)553-564
Number of pages12
JournalStochastic Models
Volume18
Issue number4
DOIs
StatePublished - 2002

Keywords

  • Compound Poisson process
  • Cycle maximum
  • Hitting probability
  • Ruin
  • Single-server queue
  • Two-sided first-exit time
  • Workload

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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