【摘要】 本文研究带有重试轨道和两类顾客的M/M/1批服务排队系统的稳态性能.该排队系统中,存在两类顾客,无优先级,但是顾客到达率和服务机制不同,服务台的服务速率与服务台内顾客类别相关.对其中一类顾客而言,系统为损失制服务系统,而另一类顾客在观察到服务台繁忙时,则以一定概率进入重试轨道.通过分析相应的马尔可夫过程,得到了系统稳态存在的充分必要条件.在该稳态条件下,利用矩阵分析方法计算得到系统的稳态概率分布、系统的平均轨道队长、服务台内的平均顾客数、顾客的平均逗留时间等重要性能指标,最后利用数值分析,展示了系统参数的变化对系统性能指标的影响.更多还原

【Abstract】 In this paper, the steady-state performance of an M/M/1 batch service retrial queuing system with two types of parallel customers is studied. In this queuing system, there are two types of customers, no priority, but the customer arrival rate and service mechanism are different. The service rate is related to the customer category in the server. For one type of customer, the system is a loss system; The other type of customer enters the orbit with a certain probability when the server is busy.By analyzing the Markov process, the sufficient and necessary conditions for the existence of the steady state of the system are obtained. Besides, we used matrix analytic method to calculate the important performance measures of this system, such as the steady-state probability distribution of the system, the mean size of service station, the mean queue length of the orbit and the mean sojourn time of an arbitrary customer. Finally, the numerical analysis is used to show the impacts of the various parameters on the system performance measures.更多还原