Repairable Queue with Non-exponential Interarrival Time and Variable Breakdown Rates

Abstract

This paper considers a single server queue in which the service time is exponentially distributed and the service station may breakdown according to a Poisson process with the rates γ and γ' in busy period and idle period respectively. Repair will be performed immediately following a breakdown. The repair time is assumed to have an exponential distribution. Let g(t) and G(t) be the probability density function and the cumulative distribution function of the interarrival time respectively. When t tends to infinity, the rate of g(t)/[1 – G(t)] will tend to a constant. A set of equations will be derived for the probabilities of the queue length and the states of the arrival, repair and service processes when the queue is in a stationary state. By solving these equations, numerical results for the stationary queue length distribution can be obtained.