Markov random field models of multicasting in tree networks
Markov random field models of multicasting in tree networks
复制标题
树状网络中多播的马尔可夫随机场模型
DOI：
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发表时间：
2002
影响因子：
1.2
通讯作者：
P. Mitra
中科院分区：
文献类型：
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作者：
K. Ramanan;Anirvan M. Sengupta;I. Ziedins;P. Mitra
在本文中，我们分析了一个支持两种类型呼叫的规则树丢失网络模型：单播呼叫和组播呼叫，其中单播呼叫需要单链路上的单位容量，多播呼叫需要节点发出的每条链路上的单位容量。我们研究了在具有统一的单播和组播到达率的大型网络的核心中呼叫分布的行为。在足够高的组播呼叫到达率下，网络表现出一种‘相变’，这导致由于组播阻塞概率的空间变化而导致的不公平性。我们研究了相变与单播到达速率、网络的协调数和网络中边的容量的奇偶性的依赖关系。数值结果表明，当链路上存在奇数和偶数容量时，相变的本质是不同的。即使在网络中引入非均匀到达速率和多跳多播呼叫，这些现象也会持续存在。最后，我们还指出了当存在多播时，诸如Erlang不动点近似之类的近似的不足。
In this paper, we analyse a model of a regular tree loss network that supports two types of calls: unicast calls that require unit capacity on a single link, and multicast calls that require unit capacity on every link emanating from a node. We study the behaviour of the distribution of calls in the core of a large network that has uniform unicast and multicast arrival rates. At sufficiently high multicast call arrival rates the network exhibits a ‘phase transition’, leading to unfairness due to spatial variation in the multicast blocking probabilities. We study the dependence of the phase transition on unicast arrival rates, the coordination number of the network, and the parity of the capacity of edges in the network. Numerical results suggest that the nature of phase transitions is qualitatively different when there are odd and even capacities on the links. These phenomena are seen to persist even with the introduction of nonuniform arrival rates and multihop multicast calls into the network. Finally, we also show the inadequacy of approximations such as the Erlang fixed-point approximations when multicasting is present.