带有止步和中途退出的M／M／1／N多重工作休假排队系统

带有止步和中途退出的M／M／1／N多重工作休假排队系统

赵晓华¹, 樊剑武², 田乃硕¹, 田瑞玲¹

1. 燕山大学理学院, 河北秦皇岛 066004; 2. 燕山大学里仁学院, 河北秦皇岛 066004

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2006-10-24 发布日期:2006-10-24
通讯作者: 赵晓华

The M／M／1／N queuing system with balking, reneging and multiple working vacations

ZHAO Xiao-hua¹, FAN Jian-wu², TIAN Nai-shuo¹, TIAN Rui-ling¹

1. College of Science, Yanshan University, Qinhuangdao, 066004, Hebei, China;2. LiRen College,Yanshan University, Qinhuangdao, 066004, Hebei, China

Received:1900-01-01 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
Contact: ZHAO Xiao-hua

摘要/Abstract

摘要：

研究了一个带有止步和中途退出的M／M／1／N多重工作休假排队系统。利用马尔科夫过程理论和矩阵解法求出了稳态概率的矩阵解,并得到了系统的平均队长、平均等待队长以及顾客的平均损失率等性能指标。最后通过数值例子分析了系统的参数,休假时的工作率μv和休假率θ对平均队长的影响。

关键词: 多重工作休假, 稳态概率, 矩阵解法, 中途退出, 止步

Abstract:

An M／M／1／N queuing system was considered with balking, reneging and multiple working vacations. First, the matrix form solution of steady-state probability was derived by the Markfov process method and the matrix solution method. Some performance measures of the system such as the expected number of customers in the system or in the queue and the average rate of the customer loss were also presented. Finally, the effect of the parameters of the system were investigated by numerical examples, such as the vacation service rate μv and the vacation rate θ on the expected queue length.

Key words: steady-state probability

, matrix solution method, reneging, balking,

multiple working vacations

中图分类号:

O226

赵晓华,樊剑武,田乃硕,田瑞玲 . 带有止步和中途退出的M／M／1／N多重工作休假排队系统[J]. J4, 2008, 43(10): 46-51 .

ZHAO Xiao-hua,FAN Jian-wu,TIAN Nai-shuo,TIAN Rui-ling .

The M／M／1／N queuing system with balking, reneging and multiple working vacations

[J]. J4, 2008, 43(10): 46-51 .

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