The M/M/N Repairable Queueing System with Variable Breakdown Rates

Abstract

This paper considers the M/M/N repairable queuing system. The customers' arrival is a Poisson process. The servers are subject to breakdown according to Poisson processes with different rates in idle time and busy time, respectively. The breakdown servers are repaired by repairmen, and the repair time is an exponential distribution. Using probability generating function and transform method, we obtain the steady-state probabilities of the system states, the steady-state availability of the servers, and the mean queueing length of the model.