带MMPP到达的两结点闭路休假排队系统分析

Analysis of a Two-Stage Closed Queueing System with Vacation and MMPP Arrival

以计算机系统实际应用为背景 ,提出了带MMPP(Markov -ModulatedPoissonPro cess)到达的两结点休假闭网络 该模型也适用于带反馈的通讯信息系统和有限工位的自适应生产系统等 MMPP是较Erlang分布和PH分布等到达间隔更为广泛的一类马尔可夫到达 ,将其引进闭路休假排队系统在已有的文献中尝未得见 ,因此 ,该研究无论从实际应用目的还是从理论研究的角度看都是十分有意义的 笔者采用了相位分解原理和笔者以前获得的结果 ,求得了所述模型的稳态分布和循环时间

Based on the praxes in actual computer systems, we give a two stage closed queueing model with vacation and MMPP (Markov modulated poisson process) arrival.The model does also fit some communication networks with feedback and a type of self adapted productive systems with finite jobs etc. MMPP arrival is a kind of more widely used Markovian arrival processes (MAPS) than that of Erlang and PH distributions. Introducing it into the two stage closed queueing systems with vacations is a matter that we have not seen up to now within literatures in hand. Therefore this work is of great significance not only for the purpose of actual applications but also for the sake of theoretical research. By using the phase decomposition principle and the results that the anther got before, we have got the steady states and the cyclic time of the model. It is another attampt to solve the problems of this type of closed systems with the related opened models.