## Abstract

We consider the one-sided and the two-sided first-exit problem for a compound Poisson process with linear deterministic decrease between positive and negative jumps. This process (X(t))_{t≥0} occurs as the workload process of a single-server queueing system with random workload removal, which we denote by M/G_{u}/G_{d}/1, where G_{u}(G_{d}) stands for the distribution of the upward (downward) jumps; other applications are to cash management, dams, and several related fields. Under various conditions on G_{u} and G_{d} (assuming e.g. that one of them is hyperexponential, Erlang or Coxian), we derive the joint distribution of τ_{y} = inf{t ≥ 0|X(t) ∉ (0,y)},y > 0, and X(τ _{y}) as well as that of T = inf{t ≥ 0|X(t) ≤ 0} and X(T). We also determine the distribution of sup{X(t)[0 ≤ t ≤ T}.

Original language | English |
---|---|

Pages (from-to) | 139-157 |

Number of pages | 19 |

Journal | Stochastic Models |

Volume | 18 |

Issue number | 1 |

DOIs | |

State | Published - 2002 |

## Keywords

- Compound Poisson process
- First-exit time
- Laplace transform
- Maximum
- Single-server queue
- Work removal

## ASJC Scopus subject areas

- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics