Article ID: | iaor20032092 |
Country: | Netherlands |
Volume: | 113 |
Issue: | 1 |
Start Page Number: | 119 |
End Page Number: | 132 |
Publication Date: | Jul 2002 |
Journal: | Annals of Operations Research |
Authors: | Zacks S., Stadje W., Perry D. |
Keywords: | markov processes |
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