Abstract:

Continuous-time single-server queues with negative and positive customers have been thoroughly investigated and applied in many multi-agent service system and computer networks. The discrete time Geo/Geo/1 queue with negative and positive customers, however, has appeared only recently in the literature. This paper analyzes a dis-crete-time single-server queue by extending the Geo/Geo/1 queue with geometrical arrival of both positive and negative customers. It also carries out the associated stationary queue length distribution and the steady-state distri-bution of the waiting time size under both removal of customer at the head (RCH) and removal of customer at the end (RCE).

Key words: G-queue, discrete-time queue, removal of customer at the head (RCH) and removal of customer at the end (RCE), GI/M/1 queue, waiting time

摘要： 带有正负顾客的连续时间单台服务器的队列系统得到深入研究且已应用于多Agent服务系统和计算机网络系统, 但带有正负顾客的离散时间Geo/Geo/1队列研究只在最近才出现。在拓展离散时间单台服务器Geo/Geo/1队列的基础上, 提出了一个具有正负几何到达顾客的离散时间单台服务器GI/M/1队列模型, 分析了队列静态长度分布和在RCH与RCE情况下的等待时间长度分布。

关键词: G队列, 离散时间队列, 移除队首和移除队尾, GI/M/1队列, 等待时间