二状态批量到达的离散时间排队系统

Analysis of discrete-time queuing system with two state batch arrival

讨论了离散时间状态下的二状态批量到达排队系统,推广了经典的离散时间排队模型.考虑在单个服务台的情形,假设二类顾客的批次到达分别服从不同参数的几何分布,二类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分布或母函数.这些结论与经典排队系统中相应的结论在形式上十分相似,并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 discrete-time queuing system with two state batch arrival is discussed on the basis of classical queuing system. On the assumption that a single server provides service to the customers in the system, and the batch arrival of the two different customers submits to the geometrical distribution, 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. These conclusions are similar to classical model which to be as a special case, and promote the framework of the random queuing system.