On the existence of finite-dimensional filters for Markov-modulated traffic
On the existence of finite-dimensional filters for Markov-modulated traffic
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关于马尔可夫调制流量的有限维滤波器的存在性
DOI：
10.2307/3215042
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发表时间：
1994
影响因子：
1
通讯作者：
J. Walrand
中科院分区：
文献类型：
--
作者：
C. Olivier;J. Walrand
马尔可夫调制泊松过程(MMPP)是一个速度为有限马氏链的泊松过程。泊松过程是一个简单的MMPP。MMPP/M/1队列是具有MMPP到达、无限容量和单个指数服务器的队列。证明了MMPP/M/1排队的输出不是MMPP过程，除非输入是泊松过程。在给定排队离开过程的情况下，我们通过分析状态的非线性滤波器的结构来得到这一结果。结果的实际意义在于，它排除了具有MMPP输入的排队网络的简单有限描述的存在。
A Markov-modulated Poisson process (MMPP) is a Poisson process whose rate is a finite Markov chain. The Poisson process is a simple MMPP. An MMPP/M/1 queue is a queue with MMPP arrivals, an infinite capacity, and a single exponential server. We prove that the output of an MMPP/M/1 queue is not an MMPP process unless the input is Poisson. We derive this result by analyzing the structure of the non-linear filter of the state given the departure process of the queue. The practical relevance of the result is that it rules out the existence of simple finite descriptions of queueing networks with MMPP inputs.