Stability Considerations for Networks

该研究将解决研究网络中出现的渐近行为和基本限制的有效方法的需求。这项工作将限于多维环境中的稳定性问题。这里使用的稳定性的定义足够广泛，可以涵盖网络行为的许多方面，如概率的有界性（即亚稳定性）、极限分布、几何遍历性、强稳定性、收敛到表模式的速度、队列长度和等待时间分布的有限矩和尾、部分稳定性、鲁棒性、截止现象、分布的形状、双稳定性、结构性质（例如一些感兴趣的参数的单调性）、渐近性能、实时系统的无饥饿状态、实际稳定性和网络行为的突然变化。本项目采用随机方法。该研究将使用基于非马尔可夫哲学的网络稳定性分析的新方法。研究表明，该方法可以为多址系统、令牌传递环、FDDI、ATM网络、一般队列网络等开放性问题的稳定性提供严格的稳定性标准。

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.