摘要
考虑具有常重试率和Bernoulli休假的M/M/1重试排队,到达系统的顾客仅知道服务台的状态.如果在顾客到达时刻服务台正忙,则顾客或以概率q加入到重试组中,或以概率1-q止步.在每次服务结束后,服务台或者以概率p开始一次休假,或者以概率1-p保持空闲状态.基于收入-支出结构,得到了个体最优进队策略,社会净收益最优进队策略和利润最优进队策略.对于这些最优进队概率的大小顺序我们给出了详细的证明.最后,给出了数值例子来阐述进队策略的影响.
This paper considers an M/M/1 retrial queue with a constant retrial rate and Bernoulli vacation, in which arriving customers are only informed about the server＇s state. If the server is busy upon the arrival instant, a customer either joins the retrial orbit with probability q or balks with complementary probability 1 - q. After each service completion, the server either begins a single vacation with probability p or remains idle with probability 1 - p. In this paper, the individual optimal joining strategy, the joining strategy for the social net welfare and the joining strategy for the optimal profit are derived under a natural reward-cost structure. We give a rigorous proof regarding the ordering of the optimal joining probabilities. Finally, some numerical examples are given to illustrate the effect of on the joining strategies.
作者
高珊
王金亭
Tien Van Do
GAO SHAN WANG JINTING DO TIEN VAN(Department of Mathematics and Statistics, Fuyang Normal University, Fuyang 236037, China Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China Department of Networked Systems and Services Budapest University of Technology and Economics, Budapest, Hungary)
出处
《应用数学学报》
CSCD
北大核心
2017年第1期106-120,共15页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金(No.61672006
71571014
71390334
11301306)
安徽省高等学校省级自然科学研究(No.KJ2014ZD21
KJ2015A182
KJ2015A191
KJ2016A875)资助项目
