Modeling and Control for Next-Gerneration Integrated-Services Networks

研究者建议通过非传统的建模和分析方法来分析下一代网络的行为和研究控制和管理问题。在未来的综合业务网络中，拥塞现象可能与互联网等更传统的系统中的拥塞现象在性质上有很大不同。原因是，在细胞水平上，远程依赖和高可变性现象将在我们通过网络分析、设计和提供服务的方式中发挥重要作用。虽然这些现象已经在现有系统中得到观察和统计分析，但预计服务的一体化将扩大这些现象。拟议研究的第一部分涉及对研究者最近发现的进一步证明，该发现解释了Levy过程如何成为某些类型的远程依赖流量的宏观模型。论证是通过严格推导交通过程概率分布的宏观近似来完成的。此外，还对分数阶布朗运动进行了比较和进一步的分析与仿真。研究者还建议明确研究这些模型（特别是Levy过程）对绩效和控制的影响。他建议使用样本路径公式和守恒定律来推导可解系统的显式解。与稳定列维运动输入串联的网络是显式可解性的有希望的候选者。在续集中，为了处理不可解决的情况，他建议研究分布和延迟的极端情况。这里涉及的任务要求将大偏差结果和应用扩展到具有反馈的网络。这项研究的影响将是理解拥堵在高度可变的环境中发生的方式，并将像风险理论一样，有助于防止网络中的灾难。所提出的控制方法涉及随机微分方程，也可以解释为产生于远程相关系统。通过研究最优控制问题，提出了缓冲区管理方案。最后，他建议研究对随机交通施加确定性或塑造监管约束的影响，推导最坏情况，并结合统计和确定性描述符。这项研究的影响将导致下一代网络描述符的进一步标准化。这样的描述对于提供服务和设计正确的定价方案是无价的。这项研究的一个相当重要的方面在于它的基本特征，它重新审视了绩效模型，并选择了简单易行的范式，这些范式可以传达给学生，也可以被行业使用。

The investigator proposes to analyze the behavior and study control and management issues for next generation networks by means of non-traditional modeling and analysis. In future integrated services networks, congestion phenomena are likely to be quite different in nature than those in more traditional systems such as the Internet. The reason is that, at the cell level, the phenomena of long-range dependence and high variability are going to play a major role in the way we analyze, design and provide services over a network. While these phenomena have already been observed and statistically analyzed in existing systems, integration of services is expected to amplify them. The first part of the proposed research deals witha further justification of the investigator's recent findings that explain how Levy processes arise asmacroscopic models of certain types of long-range dependent traffic. The justification is done by rigorously deriving macroscopic approximations of the probability distributions of the traffic processes. In addition, comparison with and further analysis and simulation of fractional Brownian motions is also proposed.The investigator also proposes to explicitly study the consequences of these models (and, in particular Levy processes) to performance and control. He proposes to use sample path formulas and conservation laws in order to derive explicit solutions of solvable systems. Networks in tandem with stable-Levy motions inputs are promising candidates for explicit solvability. In the sequel, and in order to deal with non-solvable situations, he proposes to examine extremes of distributions and delays. The tasks involved here call for extensions of large deviations results and applications to networks with feedback. The impact of this study will be the understanding of the way that congestions occur in highly variable environments and will,as in risk theory, help prevent catastrophes in networks. The proposed control methods involve stochasticdifferential equations that can also be explained as arising from long-range dependent systems. By studyingoptimal control problems, the investigator proposes to tackle buffer management schemes. Finally, he proposes to examine the impact of imposing deterministic or shaping regulatory constraints on stochastic traffic, derive worst-case scenaria and combine statistical and deterministic descriptors. The impact of this study will lead to further standardization of descriptors for next generation networks. Such descriptorsare invaluable for the provision of services and the design of correct pricing schemes. A rather significant aspect of the proposed research lies in its fundamental character in that it re-examines the performance models and opts for simple and tractable paradigms that can be communicated to students but also used by the industry.