Optimal strategy analysis of an N-policy two-phase MX/M/1 queueing system with server startup and breakdowns

Abstract

This paper deals with the optimal control policy of a single removable and unreliable server in an N-policy two-phase MX/M/1 queueing system without gating and server startups. The 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. The server is turned off each time the system empties, as and when the queue length reaches or exceeds N (threshold), 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. The distribution of the system size is derived through probability generating functions and obtained other system characteristics. Finally, the expected cost per unit time is considered to determine the optimal operating policy at a minimum cost. The sensitivity analysis has been carried out to examine the effect of different parameters in the system.