带非抢占优先权和可变服务率的离散工作休假排队

主要研究带非抢占优先权和可变服务率的离散工作休假排队系统模型.建立关于两类顾客数及系统和服务台状态的四维离散马尔科夫链,并得到了转移概率矩阵.利用拟生灭过程和高斯-赛德尔迭代法,给出了系统的平稳分布和一些重要的性能指标.通过数值例子分析系统参数对性能指标的影响.构造两类顾客的利益函数分析顾客的均衡行为,根据对社会利益的算例分析,得到了在一定范围内的最优到达率.

The discrete time working vacation queue with non-preemptive priority and variable service rates

In this paper,we mainly study a discrete time working vacation queue system with non-preemptive priority and variable service rates.We develop a four-dimensional discrete time Markov Chain(MC)which includes the number of the customers with different priorities and the state of the system and the server,and obtain the transition probability matrix.By using the quasi birth-and-death(QBD)process and the method of Gauss-Sidel iteration,we give the steady-state distribution and some main performance measures.We use the numerical examples to evaluate the effect of different parameters on the system performance measures.Finally,we analyze the equilibrium behavior of the customers by constructing the benefit functions of two types of customers.According to the social benefits function,we obtain the optimal parameters within a certain range.