Optimal Strategy Analysis of an N-policy Two- phase M/M/1 Gated Queueing System with Server Startup and Breakdowns

This paper deals with the optimal operation of a single removable and unreliable server in an Npolicy two-phase M/M/1 queueing system with gating, server startups and unpredictable breakdowns. Arrivals occur in batches according to a compound Poisson process and waiting customers receive batch service all at a time in the first phase and proceed to the second phase to receive individual service. Customers who arrive during the batch service are not allowed to enter the same batch. As soon as the system becomes empty the server leaves for a vacation of random length. When the queue length reaches a threshold value N ( N 1 ≥ ) the server is immediately turned on but is temporarily unavailable to serve the waiting batch of customers. The server needs a startup time before providing batch service in the first phase. The server is subject to breakdowns during individual service according to a Poisson process and repair times of the server follow an exponential distribution. Explicit expressions for the steady state distribution of the number of customers in the system and hence the expected system length is derived. 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 in the system. V. Vasanta Kumar et al. 564 564