讨论M/T—SPH/1排队平稳队长分布和平稳逗留时间分布的尾部衰减特征,其中T—SPH表示可数状态吸收生灭过程吸收时间的分布.在分布PGF和LST的基础上,给出了两个平稳分布衰减规律的完整分析.结果表明,当参数取不同值时,平稳队长与平稳逗留时间的尾部具有三种不同类型的衰减特征.
This paper considers tail asymptotics for stationary queue length and so- journ time distribution of M/T-SPH/1 queue, where T-SPH denotes the continuous time phase type distribution defined on a birth and death process with countably many states. By analysis of probability generation function of stationary queue length and Laplace-Stieltjes transform of stationary sojourn time, a complete characterization of the regions of system parameters for exact tail asymptotics is given. The results show that there are three types of exact tail asymptotics for the queue length and sojourn time in different regions.