Transient Analysis of Unreliable Server MX/G/1 Queue with Bernoulli Vacation Schedule and Second Optional Repair under Controlled Admissibility Policy (International Journal of Engineering and Computer Science, 2014)
In this paper, we propose to study such a model which deals with the aspects concerning the control of the arrival process with second optional repair and Bernoulli vacation schedule. The paper deals with Mx/G/1 queueing system where after completion of a service the server either goes for a vacation of random length with probability  or may continue to serve the next customer with probability , if any. Both service time and vacation time follow general distribution. Server is subject to random breakdowns according to Poisson process, followed by instantaneous repair. If the server could not be repaired with the first essential repair, subsequent optional repair is needed for the restoration of the server. Both essential and optional repair times follow exponential distribution. Unlike the usual batch arrivals queueing model, there is restriction over the admissibility of batch arrivals in which not all the arriving batches are allowed to join the queue at all times.  The restricted admissibility policy differs during a busy period and a vacation period. We obtain the time dependent probability generating functions in terms of their Laplace transforms and corresponding steady state results explicitly. In addition, some performance measures such as expected queue size and expected waiting time of a customer are also obtained. The numerical results for various performance measures are displayed via graphs.