Stability Considerations for Networks

这项研究将解决有效方法的需要， 对渐近行为和基本极限的研究， 发生在网络上。这项工作将限于稳定 多维度环境中的问题。 的定义 这里使用的稳定性足够广泛，可以涵盖 网络行为，例如概率上的有界性（即， 次稳定性），极限分布，几何遍历性， 强稳定性，表模收敛速度，有限 队长和等待时间的矩和尾 分布，部分稳定性，鲁棒性，截止现象， 分布的形状、双稳性、结构特性（例如， 一些感兴趣的参数的单调性），渐近 性能，真实的时间系统的无饥饿机制， 实际稳定性和网络行为的突然变化。一 在整个项目中假设采用随机方法。 研究 将使用新的方法来分析网络的稳定性， 都是基于非马尔可夫哲学的这项研究将 证明这种方法可以严格地提供 稳定性准则等开放问题的稳定性 多路访问系统、令牌传递环、FDDI、ATM网络， 一般的队列网络等等。

The research will address the need for effective methods for the study of the asymptotic behavior and fundamental limits that occur in networking. The work will be restricted to stability problems in a multidimensional environment. The definition of stability as used here is broad enough to cover many aspects of networking behavior such as boundness in probability (i.e. substability), limiting distributions, geometric ergodicity, strong stability, rate of convergence to table modes, finite moments and tails of the queue lengths and waiting time distributions, partial stability, robustness, cut-off phenomena, shape of distributions, bistability, structural properties (e.g. monotonicity of some parameters of interest), asymptotic performance, no-starvation regime for real time systems, practical stability, and sudden changes in network behavior. A stochastic approach is assumed through the project. The research will use new approaches to the stability analysis of networking that are based on a non-Markovian philosophy. The research will demonstrate that such an approach can rigorously provide stability criteria for such open problems as stability of multiaccess systems, token passing rings, FDDI, ATM networks, general network of queues, and so forth.