具有多重工作休假的GI/Geo/1/∞离散时间排队模型的稳定性研究  

Stability of Discrete-time Queueing Model GI/Geo/1/∞with Multiple Working Vacations

作　　者：程慧慧 王文娟 CHENG Huihui;WANG Wenjuan(College of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China)

机构地区：[1]华北水利水电大学数学与统计学院,河南郑州450046

出　　处：《河南教育学院学报（自然科学版）》2020年第4期7-14,共8页Journal of Henan Institute of Education(Natural Science Edition)

摘　　要：研究了一类具有多重工作休假的离散时间排队模型的稳定性问题。该模型系统顾客容量无限,工作休假期间,单个服务器会以不同的速率进行工作,而非完全停止工作。假设顾客单个到达且到达时间间隔服从任意分布。顾客单个服务遵循先到先服务原则。正规忙期的服务时间、休假期间的服务时间和假期时间均服从几何分布。该模型先是利用嵌入Markov链法得到其遍历的充要条件;而后利用补充变量法构造Markov链,并运用非齐次差分方程得到系统稳定时顾客到达前夕与任意时刻的队长分布母函数形式。An infinite buffer discrete-time queueing model with multiple working vacations is studied,in which customers arrive individually such that the inter-arrival times are arbitrarily distributed.A single service follows the principle of First Come First Service to customers.The single server works at a different rate rather than completely stopping working during the multiple working vacations.The service times during a service period,service time during a vacation period and vacation times are geometrically distributed.First embedded Markov chain method is used to get the necessary and sufficient condition for ergodicity of this Markov chain.Then the supplementary variable technique is used to construct Markov chain while the non-homogeneous difference equation is used to obtain the generating function of steady-state system length distributions at pre-arrival and arbitrary epochs.

关 键 词：离散时间 工作休假 嵌入Markov链 补充变量法 差分方程 

分 类 号：O211[理学—概率论与数理统计]