论文标题
带有批处理输入和负到达的排队系统
A queueing system with batch renewal input and negative arrivals
论文作者
论文摘要
本文研究了一个无限缓冲服务器排队模型，其分布式分布式服务时间和负到达。普通（正面）客户根据续订到达过程以随机大小的批量到达，并加入队列/服务器以进行服务。负到达的特征是两个独立的泊松到达流程，这是一个负面客户，它删除了正在提供服务的积极客户，以及一场灾难，通过同时删除系统中存在的所有积极客户来使系统空着。使用补充变量技术和差异方程方法，我们获得了在预交前和任意时期系统中系统中积极客户数量的稳态分布的明确公式。此外，我们讨论了一些特殊模型的结果，无论有无负到达以及它们的稳定条件。如很少的数值示例所示，在整个分析过程中获得的结果是可以在计算上处理的。此外，我们通过某些图形表示，讨论了负到达对系统性能的影响。
This paper studies an infinite buffer single server queueing model with exponentially distributed service times and negative arrivals. The ordinary (positive) customers arrive in batches of random size according to renewal arrival process, and joins the queue/server for service. The negative arrivals are characterized by two independent Poisson arrival processes, a negative customer which removes the positive customer undergoing service, if any, and a disaster which makes the system empty by simultaneously removing all the positive customers present in the system. Using the supplementary variable technique and difference equation method we obtain explicit formulae for the steady-state distribution of the number of positive customers in the system at pre-arrival and arbitrary epochs. Moreover, we discuss the results of some special models with or without negative arrivals along with their stability conditions. The results obtained throughout the analysis are computationally tractable as illustrated by few numerical examples. Furthermore, we discuss the impact of the negative arrivals on the performance of the system by means of some graphical representations.
