Asymptotic marginal independence in large networks of loss systems

Network models in which each node is a loss system frequently arise in telephony. Models with several hundred nodes are common. Suppose a customer requires a server from each of several nodes. It would be convenient if the probability that the required servers are all free were approximately a product, where each term is the probability a required node has a free server. We present some theorems to support this approximation. Most of the theorems are restricted to nodes with one server. Some of the difficulties in analyzing nodes with multiple servers are described.     

一类变分不等方程的有限元逼近

本文对一类带有两个变函数的非线性变分不等方程进行讨论，所讨论的区域Ω＝Ｒ＾ｎ是有界子开子集，边界具有分片Ｃ＾２光滑，但不必为凸区域，文中给出了解的有限元逼近及逼近的误差估计。     

Asymptotic analysis of Emden–Fowler type equation with an application to power flow models

Emden–Fowler type equations are nonlinear differential equations that appear in many fields such as mathematical physics, astrophysics and chemistry. In this paper, we perform an asymptotic analysis of a specific Emden–Fowler type equation that emerges in a queuing theory context as an approximation of voltages under a well-known power flow model. Thus, we place Emden–Fowler type equations in the context of electrical engineering. We derive properties of the continuous solution of this specific Emden–Fowler type equation and study the asymptotic behavior of its discrete analog. We conclude that the discrete analog has the same asymptotic behavior as the classical continuous Emden–Fowler type equation that we consider.