摘要
研究了带有止步和状态相依服务率的M/Ej/1多重休假排队系统,主要在多重休假排队系统中增加了止步和状态相依两个因素.通过使用矩阵几何解的方法,求出了系统的平衡条件,进一步导出了系统的稳态概率分布,并且给出了率阵R的迭代计算程序及j=2时R的精确表达式.在此基础上,还求出了稳态下系统的一些性能指标如系统的平均队长,平均等待队长,平均止步率,服务员忙的概率,服务员休假的概率等,给出了具体的表达式.
An M/Ej/1 multiple vacation queue system with balking and state-dependent service rate is studied. If a customer on arrival finds other customers in the system, it either decides to enter the queue or balks with a constant probability. Customers are served with two different rates depending on the number of customers in the system. When the number of customers in the system is less than or equal to the critical value k, the server has slow service rate, otherwise the server has fast service rate. By using the matrix geometric solution, we obtain the equilibrium condition of the system, and also derive the stationary probability of the system. We also present an algorithm of the matrix R, and give the explicit expression of R for j=2. In addition, we get some of the system performance measures, such as the expected number of customers in the system, the expected number of customers in the queue, the mean balking rate of the system, the probability that the server is busy, and give the expressions of them.
出处
《浙江工业大学学报》
CAS
2007年第5期586-590,共5页
Journal of Zhejiang University of Technology
关键词
多重休假
止步
状态相依
矩阵几何解
稳态概率
multiple vacation
balking
state-dependent
matrix geometric solution
steady-state probability
