带有负顾客的M／M／m／k-m优先权排队系统分析

J4 ›› 2011, Vol. 46 ›› Issue (11): 105-111.

带有负顾客的M／M／m／k-m优先权排队系统分析

张雷,王玉,吕胜利,马占友

燕山大学理学院, 河北秦皇岛 066004

收稿日期:2011-03-22 出版日期:2011-11-20 发布日期:2011-11-30
作者简介:张雷(1986- ),男,硕士,研究方向为排队论及其在网络中的应用.Email:zzll.peace@163.com
基金资助:
国家自然科学基金资助项目(71071133);河北省高等学校科学技术研究指导项目(Z2010182)

Analysis of the M／M／m／k-m preemptive priority queuing system with negative customers

ZHANG Lei, WANG Yu, L Sheng-li, MA Zhan-you

College of Science, Yanshan University, Qinhuangdao 066004, Hebei, China

Received:2011-03-22 Online:2011-11-20 Published:2011-11-30

摘要/Abstract

摘要：

研究了两类顾客共用一个有限容量等待空间的多服务台排队系统,其中第一类顾客具有强占优先权,第二类顾客分正顾客和负顾客两种,负顾客不接受服务且在到达系统后一对一抵消排在队尾的第二类正顾客。根据状态转移图得到了稳态下的平衡方程,利用矩阵分析理论得出了两类顾客的平均队长和溢出率,通过数值例子验证了模型的有效性,并结合图形详细分析了服务率和正、负顾客的到达率对系统各项性能指标的影响。

关键词: 多服务台;强占优先权;负顾客;平均队长;溢出率

Abstract:

A multi-server queuing system was studied with two classes of customers which shared a limited buffer. The customers of the first class had the preemptive priority,while the second class included positive and negative customers. The negative customers would not be served and the positive customers were removed one by one at the tail. According to the state transition figure, the stationary balance equations were obtained. By using matrix analysis theory, the average queuing length and the loss rate of the two classes were separately given, and a numerical example was presented to prove the effectiveness of this model. Then the influence of various parameters on the system was analyzed in combination with figures.

Key words: multi-server; preemptive priority; negative customer; average queuing length; loss rate

张雷,王玉,吕胜利,马占友. 带有负顾客的M／M／m／k-m优先权排队系统分析[J]. J4, 2011, 46(11): 105-111.

ZHANG Lei, WANG Yu, L Sheng-li, MA Zhan-you. Analysis of the M／M／m／k-m preemptive priority queuing system with negative customers[J]. J4, 2011, 46(11): 105-111.

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