RELIABILITY APPROXIMATION OF A MARKOV QUEUING SYSTEM WITH SERVER BREAKDOWN AND REPAIR

This paper considers the reliability approximation of the queueing sys tem PH/PH/1 with server breakdown and repair, where the life time of t he server has the exponential distribution, and its repair time has th e phase type distribution. First, we obtain the steady availability an d steady failure frequency of the server. Then, we get the reliability function of the server, its probability density function and its Lapl ace-Stiltjes transform, which also gives an effective approximation of the reliability function of the server, where the error of the approx imation 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 repa irable server. (C) 1997 Elsevier Science Ltd.