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具有 FCFS 服务规则,不同顾客类不同服务速率的离散系统仿真问题,无论是在理论上还是在实际中都大量碰到。尽管许多排队论学者长期致力于这方面的研究,但在解析解方面几乎毫无进展,最后不得不暂时放弃解析解想法,而寻求近似方法。然而现有的近似方法还十分不完善,它们大都无法保证收敛,无法知道精确度并存在计算工作量大等严重缺陷。特别是对 FCFS 服务规则,不同顾客类不同服务速率时,第三个缺陷尤为突出。本文对具有中央服务台形式,所有队列均为 FCFC 服务规则,不同顾客类不同路径和不同服务速率的刚络进行了研究。借助 BCMP 网络群对原系统进行无限逼近,使得等效网络与原网络误差最小。且所得算法呈递推形式,计算量极小。
The discrete system simulation problem with FCFS service rules and different service rates of different customers, whether in theory or in practice, is encountered in great quantities. Although many queuing scholars have long been committed to research in this area, there has been almost no progress in analytical solutions, and finally they have to temporarily abandon analytic solutions to seek an approximation. However, the existing approximate methods are still not perfect. Most of them can not guarantee the convergence, they can not know the accuracy and there are serious defects such as large computational workload. Especially for the FCFS service rules, different customer service rates of different classes, the third flaw is particularly prominent. In this paper, the form of a central service station, all the queues are FCFC service rules, different customer classes and different service rates of different networks. With BCMP network group, the original system is infinitely approximated so that the error between the equivalent network and the original network is minimized. And the algorithm presented in the form of recursion, the computation is minimal.