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An M/G/1 queueing model with vacation times

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  • Serie A: Theorie
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Abstract

This paper deals with an M/G/1 queueing system with finite capacity for the workload, where the workload at timet is defined as the total amount of work in the system at timet. When the server provides service he will continue servicing until the system becomes empty, after which he leaves the system for a stochastic period of time, which will be called a vacation. When the server, returning from a vacation, finds the system still empty, he leaves for another vacation, otherwise he immediately starts servicing again.

Using an embedding approach several characteristics of this system are derived amongst which the joint stationary distribution of the workload and the stage of the server.

Zusammenfassung

Diese Arbeit befaßt sich mit einem M/G/1 Wartesystem, das hinsichtlich der anstehenden Arbeit eine endliche Kapazität hat. Wenn der Bediener tätig ist, bleibt er es solange, bis das System leer ist. Danach ist er während einer stochastischen Pausenzeit nicht verfügbar. Ist am Ende einer Pausenzeit das System immer noch leer, so schließt sich eine weitere Pausenzeit an; ansonsten wird unverzüglich die Bedienung am Ende der Pausenzeit wieder aufgenommen.

Unter Verwendung eines eingebetteten Prozesses werden mehrere Kenngrößen des Systems ermittelt, darunter z.B. die gemeinsame Verteilung von anstehender Arbeit und Zustand des Bedieners.

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References

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Authors and Affiliations

  1. Interfaculty of Actuarial Sciences and Econometrics, Free University, De Boelaan, 1081, NL-Amsterdam

    F. A. van der Duyn Schouten

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  1. F. A. van der Duyn Schouten
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van der Duyn Schouten, F.A. An M/G/1 queueing model with vacation times. Zeitschrift für Operations Research 22, 95–105 (1978). https://doi.org/10.1007/BF01917651

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  • DOI: https://doi.org/10.1007/BF01917651

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