有限T-IPH/Geo/1/N排队平稳指标的数值计算

Numerical computation for stationary indices of finite T-IPH/Geo/1/N queue

讨论了T-IPH/Geo/1/N有限排队,其中T-IPH表示可数状态吸收生灭链吸收时间的分布.对该排队模型,用有限位相拟生灭(QBD)过程进行建模.首先得到了计算该QBD过程率阵非零元素的迭代公式;其次在所得结果的基础上,进一步给出了T-IPH/Geo/1/N排队平稳队长以及等待时间分布的公式.

A finite T-IPH/Geo/1/N queue system is considered, where T-IPH denotes the discrete-time phase type distribution defined on a birth and death chain with countably many states. The queue model can be described by a quasi-birth-and-death （QBD） process with finite phases. The iterative formula to calculate nonzero values in the rate matrix of the QBD process is proved firstly. Furthermore, based on the obtained results, the stationary queue length and waiting time distribution of the T-IPH/Geo/1/N queue are given.