具有工作休假的离散时间Geo/Geo/1重试排队系统  

The Discrete-Time Geo/Geo/1 Retrial Queue with Working Vacations

作　　者：彭懿[1] PENG Yi(Junior Education Department, Changsha Normal University, Changsha 410100, China)

机构地区：[1]长沙师范学院初等教育系,中国长沙410100

出　　处：《湖南师范大学自然科学学报》2017年第2期89-94,共6页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金数学天元基金资助项目(11626045);湖南省自然科学基金资助项目(2016JJ6001);湖南省教育厅资助科研项目(15C0100)

摘　　要：研究了具有工作休假的离散时间Geo/Geo/1重试排队系统.服务台具有工作休假模式,休假时间服从几何分布并且不能被打断.分析了此排队系统的马氏链,得到了系统稳态存在的充要条件.利用系统演化的平衡方程组求出了重试组队长和服务台状态的联合平稳分布.最后利用重试组队长的概率母函数,进一步得到了一系列重要的排队性能指标.The classical Geo/Geo/1 retrial queue with working vacations was studied, where working vaca- tions are geometric distributed and cannot be interrupted. The Markov chain underlying the considered queueing system was analyzed and its stability condition was derived. Using the balance equations, the steady-state joint distribution of the number of customers in the obit and the states of the server was obtained. Furthermore, the generating functions of the number of customers in the orbit was found and some performance measures of the system in the steady-state was presented.

关 键 词：离散时间重试排队系统 工作休假 拟生灭过程 

分 类 号：O122[理学—数学]