Reliability approximation of a Markov queueing system with server breakdown and repair

This paper considers the reliability approximation of the queueing system PH/PH/1 with server breakdown and repair, where the life time of the server has the exponential distribution, and its repair time has the phase type distribution. First, we obtain the steady availability and steady failure frequency of the server. Then, we get the reliability function of the server, its probability density function and its Laplace-Stiltjes transform, which also gives an effective approximation of the reliability function of the server, where the error of the approximation can be easily bounded and is uniform in t. Finally, we discuss a special case and we can show that the reliability approximation has a wider application to various Markovian queueing systems with a repairable server.