An Approximation Method for Tandem Queues with Blocking
提出一种近似方法分析服务器间有限缓冲区导致阻塞的开放串联队列系统，通过边际概率分布和条件概率近似评估，迭代求解相邻服务器对，给出单个服务器性能指标和相邻队列联合长度分布近似，迭代次数随节点数增长适度。
We propose an approximate analysis of open systems of tandem queues with blocking caused by finite buffers between servers. Our approach relies on the use of marginal probability distributions (“state equivalence”) coupled with an approximate evaluation of the conditional probabilities introduced through the equivalence. The method iterates over consecutive pairs of servers using the solution of a two-queue system as a building block. It produces performance measures for individual servers as well as an approximation to joint queue-length probability distributions for pairs of neighboring stations. Experience indicates that the number of iterations required for the method grows moderately with the number of nodes in the network. We give examples to demonstrate the accuracy and the convergence properties of the proposed approximation.