休假时间服从T-SPH分布的M/M/1单重休假排队

The M/M/1 Queue with Single T-SPH Vacations

本文研究休假时间服从T-SPH分布的M/M/1单重休假排队模型.T-SPH表示由可数状态生灭过程定义的位相型分布.该模型可以用一个具有可数位相的拟生灭(QBD)过程来描述.利用拟生灭过程和算子几何解的方法,我们给出了模型率算子的具体形式以及平稳队长分布的概率母函数.在此基础上,得到了平稳队长和平稳等待时间的随机分解结果以及附加队长的概率母函数(PGF)和附加延迟的LST的具体形式.

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 PGF of the stationary queue length. Based on the stationary queue length, we obtain the stochastic decomposition structures 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.