An $M^{[X]} / G / 1$ queue with Bernoulli schedule, general vacation times with exponential delay time, random breakdowns and exponential repairs time

  • Rehab F. Khalaf
  • Eiman J. Alenezy

Abstract

In this paper we study the batch arrival queueing system $M^{[X]}$ / $G$ / $1$ in which the server has the option to take a vacation after any service completion, when the server finished any period of vacation it does not start serving in the system and there is a period of delay time before starting the service, we assume that the delay times are exponentially distributed. The server may face random breakdowns from time to time. When the server breaks down, its repair process starts immediately We assume that the service times and vacation times are generally distributed while the breakdown times and delay times are exponentially distributed. We assume that the customers arrive to the service station in batches of variable size, but are served one by one. Using the supplementary variables technique introduced first by Cox (1955), we obtain steady state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue, the average number of customers, and the average waiting time in the queue.
Published
2011-02-15
Section
Articles