A queueing inventory system with server working breakdown

Abstract

This paper considers a single server inventory queueing system with two types of server breakdowns, say Type 1(T1) breakdown and Type 2 (T2) breakdowns, and working breakdown. T1 breakdown occurs in regular service period whereas T2 breakdown occurs in the duration of working breakdown. The inter arrival time between any two customers and the times of occurrences of both types of breakdowns are all independent exponential distributions. The commencement of repairing process of T1 breakdown follows Bernoulli’s whereas the commencement of repairing process of T2 breakdown is instantaneous. By using matrix method, we obtain the steady state probability vector of the finite capacity queueing inventory system. Finally, the numerical examination of model sensitiveness is performed.