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A direct approach to sojourn times in a busy period of an M/M/1 queue

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Abstract

In this paper we present a direct approach to obtaining joint distributions of various quantities of interest in a busy period in an M/M/1 queue. These quantities are: the sojourn times and waiting times of all the customers in the busy period, the busy period length and the number of customers served in a busy period. Since the evolution of the total workload process between two successive customer arrivals is deterministic, this work gives statistic of the complete evolution of the workload process within a busy period.

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Authors and Affiliations

  1. Dept. of Computer Science and Engineering, Indian Institute of Technology Delhi, New Delhi, India

    Arzad A. Kherani

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  1. Arzad A. Kherani
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Correspondence to Arzad A. Kherani.

Additional information

This work was done when the author was post doctoral fellow with the MAESTRO group at INRIA, Sophia Antipolis, France, and was supported by project no. 2900-IT-1 from the Centre Franco-Indien pour la Promotion de la Recherche Avancee (CEFIPRA).

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Kherani, A.A. A direct approach to sojourn times in a busy period of an M/M/1 queue. Queueing Syst 53, 159–169 (2006). https://doi.org/10.1007/s11134-006-6989-x

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  • DOI: https://doi.org/10.1007/s11134-006-6989-x

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