Optimal Strategy Analysis of an N-Policy Two-Phase M/Ek/1 Queueing System with Server Breakdowns and Gating

Two-phase M/Ek/1 queueing system with N -policy for exhaustive batch service with gating, and server startups and breakdowns is studied in this paper. The customers arrive individually according to a Poisson process and waiting customers receive batch service all at a time in the first phase and are served individually in the second phase. The server is turned off each time the system empties, as and when the queue length reaches or exceeds 3262 V. Vasanta Kumar, B.V.S.N. Hari Prasad, K. Chandan and K.P.R.Rao N (threshold) batch service starts. Before the batch service, the system requires a random startup time for pre-service. As soon as the startup period is over the server starts the batch service followed by individual service to all customers in the batch. It is assumed that the server may breakdown during individual service according to a Poisson process and the repair times has an exponential distribution. Explicit expressions for the steady state distribution of the number of customers in the system are obtained and also derived the expected system length. The total expected cost function is developed to determine the optimal threshold of N at a minimum cost. Numerical experiment is performed to validate the analytical results. The sensitivity analysis has been carried out to examine the effect of different parameters.