Nonmonotonicity of phase transitions in a loss network with controls
Nonmonotonicity of phase transitions in a loss network with controls
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带控制的损耗网络中相变的非单调性
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
I. Ziedins
中科院分区：
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作者：
B. Luen;K. Ramanan;I. Ziedins
我们考虑一个对称树丢失网络，该网络支持到最近邻居的单链路(单播)和多链路(多播)呼叫，并且在每条链路上具有容量$C$。网络运行控制，使得以任何节点为中心的多播呼叫的数量不能超过$C_V$，并且链路上的单播呼叫的数量不能超过$C_E$，其中$C_E$、$C_Vleq C$。证明了无限树上Gibbs测度的唯一性等价于相关映射的某些递推的收敛。对于$C_V=1$和$C_E=C$的情况，我们精确地刻画了相变面，并证明了在多播呼叫到达率方面，相变总是非单调的。该模型是具有硬约束的系统的一个例子，该系统的权重既附加在网络的边上，也附加在网络的节点上，并且可以被视为统计力学和组合学中出现的核心模型的推广。所得到的一些结果也适用于比损失网络更一般的模型。这些证明依赖于概率论和动力系统的技术组合。
We consider a symmetric tree loss network that supports single-link (unicast) and multi-link (multicast) calls to nearest neighbors and has capacity $C$ on each link. The network operates a control so that the number of multicast calls centered at any node cannot exceed $C_V$ and the number of unicast calls at a link cannot exceed $C_E$, where $C_E$, $C_Vleq C$. We show that uniqueness of Gibbs measures on the infinite tree is equivalent to the convergence of certain recursions of a related map. For the case $C_V=1$ and $C_E=C$, we precisely characterize the phase transition surface and show that the phase transition is always nonmonotone in the arrival rate of the multicast calls. This model is an example of a system with hard constraints that has weights attached to both the edges and nodes of the network and can be viewed as a generalization of the hard core model that arises in statistical mechanics and combinatorics. Some of the results obtained also hold for more general models than just the loss network. The proofs rely on a combination of techniques from probability theory and dynamical systems.