AVAILABILITY ANALYSIS OF THE QUEUEING SYSTEM GI/PH/I WITH SERVER BREAKDOWNS

In the existing literature of Repairable Queueing Systems (RQS), i.e., queueing 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.     

ON THE TRANSIENT DEPARTURE PROCESS OF M^x/G/1 QUEUEING SYSTEM WITH SINGLE SERVER VACATION

This paper studies the transient departure process of M^x/G/1 queueing system with single server vacation. We present a simple probability decomposition method to derive the expected number of departures occurring in finite time interval from any initial state and the asymptotic expansion of the expected number. Especially, we derive some more practical results for some special cases.