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

  • Authors:

  • Arzad A. Kherani

  • Affiliations:

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

  • Venue:
  • Queueing Systems: Theory and Applications
  • Year:
  • 2006

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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.