Tandem Retrial Queueing System with Correlated Arrival Flow and Operation of the Second Station Described by a Markov Chain
Tandem Retrial Queueing System with Correlated Arrival Flow and Operation of the Second Station Described by a Markov Chain
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马尔可夫链描述的具有相关到达流量和第二站操作的串联重审排队系统
DOI：
10.1007/978-3-642-31217-5_39
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
V. Klimenok
中科院分区：
文献类型：
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作者：
C. Kim;A. Dudin;V. Klimenok
串联队列是描述各种通信系统和网络中信息传输的很好的数学模型。这些队列对于验证为研究更一般的排队网络而设计的不同分解算法也起着重要的作用。因此，它们的研究具有重要的理论意义和应用价值。在本文中，我们认为串联队列适合于对信息流相互关联和突发性的系统和网络进行建模，这在许多现代电信网络中是典型的。通过考虑批量马尔可夫到达过程(BMAP)作为系统的输入流，考虑了客户到达间隔时间和批量到达之间的可能相关性。该系统由两个站组成。假设站1处的服务时间总体上是分布的。该站点没有缓冲区，遇到繁忙服务器的客户会以随机的时间间隔反复尝试进入系统。假设站2处的服务过程由具有有限状态空间的连续时间马尔可夫链来描述。例如，如果站2具有有限的缓冲器，该缓冲器由有限数量的相同或不同类型的服务器组成，其中服务时间分布被假设为PH(阶段)类型，则该假设成立。正在研究在1号站的服务完成时刻嵌入的马尔可夫链和任意时刻的系统状态的过程。给出了计算稳态概率的遍历条件和算法。
Tandem queues are good mathematical models for description of information transmission in various communication systems and networks. These queues play also an important role for the validation of different decomposition algorithms designed for investigating more general queueing networks. So, their investigation is interesting for theory and applications. In this paper, we consider tandem queue suitable for modeling the systems and networks where information flows are correlated and bursty what is typical for many modern telecommunication networks. Possible correlation of customers inter-arrival times and batch arrivals are taken into account via of consideration of theBatch Markovian Arrival Process(BMAP) as input stream to the system. The system consists of two stations. The service time at the station 1 is assumed to be generally distributed. There is no buffer at this station, and customers who meet the busy server repeat attempts to enter the system in random time intervals. The service process at the station 2 is assumed to be described by the continuous time Markov chain with a finite state space. This assumption holds good, e.g., if the station 2 has a finite buffer, consists of a finite number of identical or heterogeneous servers where the service time distribution is assumed to be ofPH(PHase) type. Markov chain embedded at service completion epochs at the station 1 and the process of system states at arbitrary time are under study. Ergodicity condition and algorithms for computing the steady state probabilities are presented.