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 |
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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
- General Decision Sciences
- Management Science and Operations Research