高负荷循环交通网络模型

把Peterson和Wein的交通网络模型推广到循环交通网络模型,在高负荷的条件下对该系统进行了分析。通过引入在排队网络中广泛使用的泛函中心极限定理的结论和多维反射的布朗运动工具,构造出该模型中网输入过程、队长过程和离去过程的表达式。在高负荷的条件下,通过与原来的交通模型相比较,获得了该系统中网输入过程、队长过程和离去过程的反射布朗运动极限。结果表明,反射的布朗运动和泛函中心极限定理是研究队列网络模型的有效方法。

Cyclic transportation network model in heavy traffic

A model of transportation system introduced by Peterson and Wein was extended to a model of cyclic transportation network system. The system in heavy traffic was analyzed by adapting functional central limit theorem results and construction of multidmensional refected Brownian motion that have been developed for queueing networks. The explicit of netput process, queuelength process and departure process of the system was presented. The reflected Brownian motion limit was achieved. The results indicate that functional central limit theorem and reflected Brownian motion could be an effective measurement for studying queueing network models.