is paper considers the M/M/ repairable queuing system. e customers' arrival is a Poisson process. e servers are subject to breakdown according to Poisson processes with different rates in idle time and busy time, respectively. e breakdown servers are repaired by repairmen, and the repair time is an exponential distribution. Using probability generating function and transform method, we obtain the steady-state probabilities of the system states, the steady-state availability of the servers, and the mean queueing length of the model.
This paper studies the single server repairable queueing system with variable service rate and failure rate. The rule of variation of the service rate is that the service rate changes when the number of customers in the system reaches a certain value. The server may fail at any time, and the failure rates of idle periods and busy periods are different. The system has one reliable repairman to repair the failure server. The steady-state joint distribution of the customers number and server states is obtained by the matrix geometric solution method, the steady-state availability of the server and significant queue performances measures are evaluated. Two special cases are analyzed, and some numerical experiments are given for the illustrations of the parameters effect.
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