State Dependent M/$H_{k}$/1/N Queueing System With Service Interruption

Abstract

The objective of this paper is to analyze M/$H_{k}$/1 queueing system with setup and unreliable server for both finite and infinite capacity under N-policy. The customers arrive to the system in accordance with Poisson process. The service times follow the k-type hyper exponential distribution. The breakdown and repair times are assumed to follow a negative exponential distribution. The arriving customers may balk, depending upon the number of customers present in the system. The generating function method is used to derive queue size distribution of the number of the customers present in the system. The cost function has been derived in term of cost elements related to different situations in order to determine the optimal operating policy. To explore the effects of various parameters on cost and other indices, the sensitivity analysis is carried out by taking numerical illustrations.