J4 ›› 2010, Vol. 45 ›› Issue (2): 37-43.
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孙贵勇 朱翼隽
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国家自然科学基金资助项目(70571030)
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摘要:
研究了一个带有N策略、负顾客和反馈的多重休假Geo/Geo/1离散时间排队系统。服务的开始由N策略确定,到达的负顾客不接受服务,只抵消正在接受服务的正顾客,若系统处于假期,则到达的负顾客自动消失。完成服务的正顾客以一定的概率反馈到队尾寻求再次服务。利用拟生灭过程和矩阵几何解的方法得到了队长稳态分布的存在条件和表达式,系统处于假期和忙期的概率以及稳态下系统队长的条件随机分解和由休假引起的附加队长的分布表达式。
关键词: 离散时间排队;负顾客;N策略;矩阵几何解;条件随机分解
Abstract:
A queue of Geo/Geo/1 model with N-policy, negative customers, feedback and multiple vacations is discussed. The starting time of service is determined by N-policy. Negative customers needn’t accept service, only removing the positive customer who is accepting service one by one. When a negative customer arrives and the system is on vacation, it will automatically disappear. Just after completion of its service, the positive customer may feeds back for the next service with certain probability. The equilibrium condition and concise expression of the steady-state distribution for the queue length are obtained by using QBDprocess and matrix-geometric solution method as well as the probability when the system is on vacation or busy. Meanwhile, the conditional stochastic decomposition structure of the queue length in steady state and the distribution of additional queue length caused by vacations are also acquired.
Key words: discrete-time queue; negative customer; N-policy; matrix-geometric solution; conditional stochastic decomposition
孙贵勇 朱翼隽. N策略、负顾客、反馈Geo/Geo/1多重休假排队模型[J]. J4, 2010, 45(2): 37-43.
SUN Gui-Yong, ZHU Yi-Juan. The Geo/Geo/1 queue model with N-policy、 negative customer、 feedback and multiple vacation[J]. J4, 2010, 45(2): 37-43.
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