• PERFORMANCE ANALYSIS OF AN N-POLICY M/EK/1 QUEUEING SYSTEM WITH SERVER START UP, UNRELIABLE SERVER AND BALKING

Abstract

This paper studies the optimal control of a non reliable and removable server in an N-policy M/Ek/1 queueing system with server start up and balking. When the queue length reaches N (N≥1), the server is immediately turned on but is temporarily unavailable to serve the waiting units. The server needs a startup time before providing the service. It is assumed that server breakdowns according to a Poisson process and the repair time have an exponential distribution. Arriving customers may balk with a certain probability and may depart without getting service due to impatience. Lack of service occur where the server is busy or due to sudden breakdown. Explicit expression for the number of units in the system are obtained and also derived various system measures. The total expected cost function is developed to determine the optimal threshold N at a minimum cost. The sensitivity analysis is performed to examine the effect of various parameters in the system.