对一类离散时间休假排队平稳指标的数值计算与渐近分析

Numerical Computation and Tail Asymptotic for Stationary Indices of a Discrete-Time Vacation Queue

摘要: 本文研究休假时间服从~T-IPH~分布的~Geo/Geo/1~休假排队,其中~T-IPH~分布是由可数状态吸收生灭链定义的离散时间无限位相分布.对多重休假和单重休假两种情形, 基于系统平稳方程和复分析方法,首先得到了排队系统平稳队长和平稳逗留时间的概率母函数~(PGF);其次, 通过对~PGF~分析,进一步得到了平稳附加队长和附加逗留时间分布律的迭代计算结果和渐近结果;最后, 通过数值例子说明了方法的有效性.

Abstract: In this paper we study a Geo/Geo/1 queue with T-IPH vacations, where T-IPH denotes the discrete-time phase type distribution defined on a birth and death process with countably many states. Both the multiple and single vacation strategies are considered. For each case, based on the system of stationary equations and using complex analysis method, we firstly give the probability generating functions (PGFs) of stationary distributions for queue length and sojourn time. Moreover, by analysis the PGFs, recursive and asymptotic formulas for additional queue length and additional delay are also given. Finally, we further give some numerical examples to show the effectiveness of the method.