Boundary crossing for the difference of two ordinary or compound Poisson processes
Autor(en): | Perry, D Stadje, W Zacks, S |
Stichwörter: | boundary crossing; busy period; compound Poisson process; cycle maximum; deterministic service time; M/G/1 QUEUES; NEGATIVE CUSTOMERS; Operations Research & Management Science; POLLACZEK-KHINTCHINE FORMULA; queue with negative customers; sided stopping time; two; WORK REMOVAL | Erscheinungsdatum: | 2002 | Herausgeber: | KLUWER ACADEMIC PUBL | Journal: | ANNALS OF OPERATIONS RESEARCH | Volumen: | 113 | Ausgabe: | 1-4 | Startseite: | 119 | Seitenende: | 132 | Zusammenfassung: | 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 t, given the busy period is longer than t. |
Beschreibung: | 1st Madrid Conference on Queueing Theory (MCQT 02), UNIV COMPLUTENSE MADRID, MADRID, SPAIN, JUL 02-05, 2002 |
ISSN: | 02545330 | DOI: | 10.1023/A:1020957827834 |
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geprüft am 01.06.2024