## 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 ± 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 language | English |
---|---|

Pages (from-to) | 119-132 |

Number of pages | 14 |

Journal | Annals of Operations Research |

Volume | 113 |

Issue number | 1-4 |

DOIs | |

State | Published - 2002 |

## Keywords

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

## ASJC Scopus subject areas

- Decision Sciences (all)
- Management Science and Operations Research