an:06091251
Zbl 1265.60184
Zhang, Hongbo; Wang, Hongwei
The M/M/1 queue with single T-SPH vacations
ZH
Chin. J. Eng. Math. 28, No. 6, 803-811 (2011).
00308147
2011
j
60K25 90B22
M/M/1 queue; T-SPH distribution; single vacation; operator-geometric solution; stochastic decomposition
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.