通信网络中的亚稳态

摘要：

Gibbens等人和Antunes等人提出的两种损失网络模型，已知表现出具有几个稳定平衡的平均场限制机制。根据Freidlin和Wentzell的随机扰动动力系统的大偏差方法，重新审视这些模型。假设他们的一些结果仍然保持在稍微放松的条件下，亚稳性质推导出这两个系统。一个李雅普诺夫函数展示Antunes等人。接下来确定与准势略有修改，渐近可逆，马尔可夫扰动相同的动力系统。另一种解释，在熵耗散，这个李雅普诺夫函数最后给出。这个论点延伸到另一个类似但封闭的模型。

英文摘要：

Two models of loss networks, introduced by Gibbens et al. and by Antunes et al., are known to exhibit a mean field limiting regime with several stable equilibria. These models are reexamined in the light of Freidlin and Wentzell's large deviation approach of randomly perturbed dynamical systems. Assuming that some of their results still hold under slightly relaxed conditions, the metastability property is derived for both systems. A Lyapunov function exhibited by Antunes et al. is next identified with the quasipotential associated with a slightly modified, asymptotically reversible, Markovian perturbation of the same dynamical system. Another interpretation, in terms of entropy dissipation, of this Lyapunov function is finally given. The argument extends to another, similar but closed model.

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