• OPTIMAL STRATEGY ANALYSIS OF AN N-POLICY TWO-PHASE M/EK/1 QUEUEING SYSTEM WITH SERVER STARTUP AND BREAKDOWNS

Abstract

This paper studies a two-phase M/Ek/1 queueing system with N-policy for exhaustive batch service, server startup and breakdowns. 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. When the queue length reaches or exceeds N (threshold), the 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 which is followed by individual service to all customers in the batch. It is assumed that the server may breakdown during individual service following Poisson process and the repair time follows an exponential distribution. Explicit expressions for the steady state distribution of the number of customers in the system and expressions for the expected system length are derived. The total expected cost function is developed to determine the optimal threshold of N at a minimum cost. Sensitivity analysis is carried out through numerical illustrations.