Stability Considerations for Networks

这项研究将解决对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。这项工作将仅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以覆盖联网行为的许多方面，例如概率上的有界性(即次稳定性)、极限分布、几何遍历、强稳定性、收敛到表模的速率、队列长度和等待时间分布的有限矩和尾部、部分稳定性、稳健性、切断现象，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、实时系统的无饥饿机制、实际稳定性以及网络行为的突然变化。在整个项目中，假设采用随机方法。这项研究将使用基于非马尔科夫哲学的新方法来分析网络的稳定性。研究表明，这种方法可以严格地为多址系统的稳定性、令牌传递环、FDDI、ATM网络、一般排队网络等公开问题提供稳定性判据。

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.