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The longest service time in a busy period

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Abstract

This paper considers the supremumm of the service times of the customers served in a busy period. For theG/G/s queue the tail behaviour of the distributionm (w) ofm is compared with that of the service time distribution. For theE k /G/1 queue an expression for the joint distribution ofm and of the number of customers served in the busy period is derived.

Finally some detailed results for theM/M/1 queue are mentioned.

Zusammenfassung

Diese Arbeit befaßt sich mit dem Supremumm der Bedienungszeiten der in einer Arbeitsperiode bedienten Kunden. Im Falle des BedienungssystemsG/G/s werden die Wahrscheinlichkeiten für große Werte vonm verglichen mit den Wahrscheinlichkeiten für große Bedienungszeiten. Im Falle vonE k /G/1 wird ein expliziter Ausdruck für die gemeinsame Verteilung vonm und der Anzahl der in der Arbeitsperiode bedienten Kunden gewonnen. Einige Resultate fürM/M/1 bilden den Abschluß.

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References

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Authors and Affiliations

  1. Mathematical Institute, University of Utrecht, Budapestlaan 6, 2506, Utrecht, The Netherlands

    O. J. Boxma

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  1. O. J. Boxma
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Boxma, O.J. The longest service time in a busy period. Zeitschrift für Operations Research 24, 235–242 (1980). https://doi.org/10.1007/BF01919902

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  • DOI: https://doi.org/10.1007/BF01919902

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