摘要
本文研究带反馈的具有正、负两类顾客的M/M/1工作休假排队模型。工作休假策略为空竭服务多重工作休假。负顾客一对一抵消队首正在接受服务的正顾客(若有),若系统中无正顾客时,到达的负顾客自动消失,负顾客不接受服务。完成服务的正顾客以概率p(0<p≤1)离开系统,以概率1-p反馈到队尾寻求再次服务。使用拟生灭过程和矩阵几何解方法得到了系统队长的稳态分布,证明了系统队长随机分解结果并给出稳态下系统中正顾客的平均队长。
The paper deals with an M/M/1 feedback queue with working vacations in which customers are either ＂positive＂ or ＂ negative＂. The working vacation policy is exhaustive service and multiple working vacations. Negative customers remove positive customers only one by one at the head （ if present）. When a negative customer arrives, if the system is empty, it will disappear. Negative customers need no services. Just after comple- tion of his service, a positive customer may leave the system with probabilityp （0 〈 p ≤ 1 ）, or feedback with probabilityl -p. Using QBD （quasi birth and death） process and matrix-geometric solution, we obtain the stead y-state distributions for the number of customers in the system and prove the result of stochastic decomposition of the queue length and gain the mean of the system size of positive customers.
出处
《运筹与管理》
CSCD
2008年第3期64-69,共6页
Operations Research and Management Science
基金
国家自然科学基金资助项目(70571030,10571076)
关键词
排队
稳态分布
随机分解
拟生灭过程
矩阵几何解
负顾客
反馈
工作休假
queue
steady-state distributions
stochastic decomposition
QBD process
matrix-geometric solution
negative customers
feedback
working vacations
