In the existing literature of Repairable Queueing Systems (RQS), i.e., queueirig systems with server breakdowns, it is almost all assumed that interarrival times of successive customers are independent, identically exponentially distributed. In this paper, we deal with more generic system GI/PH/1 with server's exponential uptime and phase-type repair time. With matrix analysis theory, we establish the equilibrium condition and the characteristics of the system, derive the transient and stationary availability behavior of the system.

In the existing literature of Repairable Queueing Systems (RQS), i.e., queueirig systems with server breakdowns, it is almost all assumed that interarrival times of successive customers are independent, identically exponentially distributed. In this paper, we deal with more generic system GI/PH/1 with server's exponential uptime and phase-type repair time. With matrix analysis theory, we establish the equilibrium condition and the characteristics of the system, derive the transient and stationary availability behavior of the system.