Cost Analysis Approach-the \(M^x / M / 1\) Queues with Working Breakdowns and Interruptions

Abstract

In this paper, we have studied the steady-state analysis of single-server Markovian bulk arrival queueing systems with working breakdowns and interruptions. For this model, the probability-generating functions of the system size distributions in steady state are obtained. Various important characteristics of the model, like the expected number of customers in the system, the expected waiting time of a customer in the system, etc., are derived. In steady state, we have discussed some important performance measures of the system and provided some numerical examples to show that our results are computationally tractable. The suitability of the model is tested in a cost optimization issue where the mean number of customers is optimized by reducing the average cost per unit hour using a direct search technique.