A Markov chain description of a workstation with infinite capacity
Autor(en): | Stadje, W | Stichwörter: | busy period; discrete time; first-entrance problem; infinite capacity; Markov chain; Mathematics; Mathematics, Applied; maximum occupation; Operations Research & Management Science; QUEUES; stationary distribution; workstation | Erscheinungsdatum: | 2003 | Herausgeber: | TAYLOR & FRANCIS LTD | Enthalten in: | OPTIMIZATION | Band: | 52 | Ausgabe: | 2 | Startseite: | 201 | Seitenende: | 210 | Zusammenfassung: | We present a discrete-time model for a workstation with infinite operating capacity at which one job arrives at every time instant and starts being processed. The jobs stay in the system for a possibly truncated geometrically distributed time period. We introduce and analyze a Markov chain which gives at any time a complete description of the state of the work on all jobs. Its positively recurrent states are the dyadic numbers in (0, 1]; we give its stationary distribution explicitly. For the busy period analysis of the workstation we study first-entrance problems of this Markov chain. |
ISSN: | 02331934 | DOI: | 10.1080/0233193031000079847 |
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geprüft am 07.06.2024