批量到达的离散时间排队系统

主要讨论了离散时间状态下的批量到达排队系统,推广了经典的离散时间排队模型.考虑单个服务台的情形,假设顾客的批次到达服从几何分布、每批到达的顾客数服从一般的离散分布、顾客的服务时间也服从几何分布,使用嵌入Markov链的方法,分析得到了该随机排队系统的队长、等待队长、等待时间以及忙期等关键指标的母函数.这些结论与经典排队系统中相对应的结论在形式上十分相似,并且将经典排队系统作为其特例,从而推广了随机排队系统的研究框架.

The analysis of discrete-time queueing system with batch arrival

The paper considered the discrete-time queueing system with batch arrival on the basis of the classical queueing system.On the assumption that a single server provides service to the customers in the system,and the batch arrival of the customers submits to the geometrical distribution,the number of the customers in a batch arrival is random variables and has the generalized distribute function,and the service time also depends on the geometrical distribution,using the method of embedded the Markov chain,the distribution functions of the queue length and the waiting queue length were described.Then,the waiting time of the queueing system was characterized and the distribution of the busying time was obtained.These conclusions are similar to that of the classical queueing system.