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The M/M/1 queue with single T-SPH vacations. (Chinese. English summary) Zbl 1265.60184
Summary: This paper considers an M/M/1 queue with single vacations where the vacation time follows the T-SPH distribution, which denotes the phase type distribution defined on a birth and death process with countably many states. This queueing system can be described by a quasi-birth-and-death (QBD) process with countably states. According to the QBD process and the operator-geometric method, we give the closed-form of the rate operator and the probability generating function (PGF) of the stationary queue length. Based on the stationary queue length, we obtain the stochastic decomposition structure of the stationary queue length and the waiting time of the model, as well as the PGF of the additional queue length and the LST of the additional delay.
Reviewer: Reviewer (Berlin)
##### MSC:
 60K25 Queueing theory (aspects of probability theory) 90B22 Queues and service in operations research