Analysis of the N-policy GI/M/1/K Queueing Systems with Working Breakdowns and Repairs. (26th May 2018) - Yang, Dong-Yuh; Cho, Yi-Chun
Abstract: In this paper, we present an algorithmic approach to the analysis of the finite-capacity GI/M/1 queue with working breakdowns under N -policy. When there are no customers in the system, the server is turned off. If the number of customers in the system reaches threshold N, then the server is turned on and working. The recently introduced working breakdown involves serving newly arrived customers at a lower service rate in cases where the server breaks down. Service times during busy and breakdown periods are exponentially distributed. When a breakdown occurs, the failed server is not repaired until there are no customers remaining in the system. In this type of queueing system, we compute the steady-state probabilities at arbitrary and pre-arrival epochs using the supplementary variable method. We propose an algorithm for computing the steady-state probabilities at pre-arrival epochs and develop system performance measures. Finally, numerical analysis is used to evaluate the effects of various system parameters on system performance measures.