The SM/PH/1 queue with repairable server of phase type life time

Abstract

We consider the reliability problem of the SM/PH/1 queue with repairable server of PH life time and PH repair time. The generalized service times are proved to be dependent on each other and not to have the same distribution if the system is at transient state. For this reason the transient behavior of the system is so complex that we can not give any available results. On the contrary, the repairable queueing system is shown to be equivalent to the classical SM/SM(PH)/1 queue when the system is at steady state, where SM(PH) denotes Markovian semi-Markov process which was discussed in Latouche [10] and Sengupta [23]. By means of the equivalent model SM/SM(PH)/1, the explicit expressions of the reliability quantities are derived, for instance, the steady state availability and the steady state failure frequency.