The generalized Mx/G (M/G)/1 (M/G) repairable queueing system (I) – some queueing indices

We consider a type of the generalized Mx/G (M/G)/1 (M/G) repairable queueing system in which the vacation time, service time, repair time and the delay vacation time are all arbitrary distributions. By using the server busy period and taking a Laplace transformation we directly obtain the recursion formula of the Laplace transformation of the transient queue length distribution at time t, the recursion formula of the equilibrium distribution, and also obtain the probability generating function of the queue length, while simultaneously pointing out the errors in the paper of Shi Dinghua in 1994.