摘要
研究了带有止步和中途退出的M/M/R/N同步多重工作休假排队系统,利用马尔可夫过程理论和矩阵解法求出了含有两个逆阵的系统稳态概率的矩阵解,并得到了系统的平均队长、服务员处在工作休假期的概率以及顾客的平均止步率等性能指标.最后通过数值例子分析了系统的参数对平均队长的影响.
An M/M/R/N queueing system was considered with balking, reneging and synchronous multiple working vacations. By using the Markfov process method and the matrix solution method,we obtain the matrix solution of steady-state probability presented by the inverse of two matrices.We also derive some performance measures of the system such as the expected number of customers in the system ,the probability of the servers in the working vacation period and the average rate of the customer who didn＇t enter the queue. Finally~ the effect of the parameters of the system on the expected queue length were investigated by numerical examples.
出处
《数学的实践与认识》
CSCD
北大核心
2011年第19期142-149,共8页
Mathematics in Practice and Theory
基金
国家自然科学基金(71071133)
关键词
排队系统
止步
中途退出
工作休假
稳态概率
queueing system
balk
reneg
working vacations
steady-state probability
