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Queueing Systems

, Volume 45, Issue 2, pp 135–160 | Cite as

The Analysis of a General Input Queue with N Policy and Exponential Vacations

  • Jau-Chuan Ke
Article

Abstract

This paper studies a single removable server in a G/M/1 queueing system with finite capacity where the server applies an N policy and takes multiple vacations when the system is empty. We provide a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining interarrival time, to develop the steady-state probability distributions of the number of customers in the system. The method is illustrated analytically for exponential and deterministic interarrival time distributions. We establish the distributions of the number of customers in the queue at pre-arrival epochs and at arbitrary epochs, as well as the distributions of the waiting time and the busy period.

recursive method steady-state probability supplementary variable vacations 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Jau-Chuan Ke
    • 1
  1. 1.Department of StatisticsNational Taichung Institute of TechnologyTaiwan, R.O.C.

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