M/G/1Repairable Oucueing System With N-policv And Warm Standby Failure

In this paper, the M/G/1repairable queueing system with N-policy andwarm standby failure is established by introducing “the service station may fails inwarm standby during idle period” and assuming that the service station can’t be repairedimmediately under warm standby condition. By using the total probabilitydecomposition, L-transform, generating function and other tools, the recursionexpressions of the queue-length distribution (the transient queue distribution and theequilibrium queue distribution), the steady customer waiting/residence time and somesystem reliability indices are discussed from any initial state. These indices include:①The probability that the time t is in the "server generalized busy time";②Theprobability that the first type failure happens and the probability that the second typefailure happens and the unavailability of the service station separately;③The expectednumbers of the first type failure and the second type failure during the interval (0,t]；④The probability that the time t is for repairing in the warm standby failure waiting.