Copula-based Dependence Modeling for Computer and Communication Networks

随着网络技术的飞速发展，互联网已经成为现代社会不可或缺的一部分。在不到50年的时间里，互联网不仅成为娱乐、通信、社交的主要平台，而且成为许多新商业服务的主要驱动力。在互联网上各种应用程序的背后，是支持其平稳运行的核心数学模型和算法。改进核心模型和算法将对整个互联网生态系统产生重大影响。因此，我们有动力研究对许多互联网应用程序未来成功至关重要的基本模型。*回顾历史，我们发现，在互联网研发的每个阶段都提出了各种依赖模型。从理论上讲，互联网流量依赖模型与排队论一起，为现代计算机网络的性能分析奠定了理论基础。在实践中，依赖模型是流量工程、网络容量规划和基于预测的资源配置的基础。总体而言，互联网本质上依赖于各种依赖模式。*虽然对计算机和通信网络的相关性建模已经做了大量的工作，但网络流量中丰富的相关性结构，特别是那些超出线性相关性范围的结构，还没有得到充分的研究。NSERC的这项发现提案的目标是通过探索Copula的力量来推动最先进的技术。Copula是一种相关性模型，能够捕捉网络业务流之间/内部的功能相关性，并在流量预测、自动资源调整和网络采样方面显示出良好的结果。通过数学分析、模拟和真实世界实验，该项目将解决两个相互交织的研究主题：基于Copula的网络性能层析成像和相互依赖的网络的Copula模型。在第一个主题中，我们将开发一种可靠的网络层析成像方法，该方法可以根据少量监控点的观测来推断网络性能。在第二个主题中，我们将研究相互依赖的网络系统，其中一个网络的性能取决于其他网络的性能。*这项研究将丰富计算机和通信网络的依赖建模工具集，并将有益于许多现实世界的应用，例如实时多媒体传输、大规模在线广播的性能监控和智能电网通信。通过将理论结果应用到我们与加拿大工业合作伙伴的现有项目中，我们的研究成果可以为加拿大的IT行业提供更有效的数据相关性分析算法。

With the fast advance of network technologies, the Internet has become an indispensable part of modern society. In less than 50 years, the Internet has become not only the major platform for entertainment, communication, and social networking, but also the main driving force for many new business services. Under the hood of diverse applications over the Internet are core mathematical models and algorithms that support their smooth operation. Improving the core models and algorithms will create a significant impact on the whole ecosystem of the Internet. We are thus motivated to investigate fundamental models that are critical to the future success of many internet applications. ******Looking back at history, we find that various dependence models have been proposed in every stage of research and development in the Internet. In theory, Internet traffic dependence models, together with queueing theory, lay the foundation for theoretical performance analysis of modern computer networks. In practice, dependence models are the basis for traffic engineering, network capacity planning, and prediction-based resource provisioning. Overall, the Internet essentially relies on various dependence models. ******While extensive work has been done on dependence modeling for computer and communication networks, the rich dependence structures in network traffic, particularly those beyond the scope of linear dependence, have not been fully explored. The goal of this NSERC discovery proposal is to push the state-of-the-art by exploring the power of copulas. Copulas are dependence models that are able to capture the functional dependence between/within network traffic flows and have shown promising results in traffic prediction, automatic resource adjustment, and network sampling. With mathematical analysis, simulation, and real-world experiments, the project will address two interweaving research themes: copula-based network performance tomography, and copula models for interdependent networks. In the first theme, we will develop a reliable network tomography method which can infer the network performance based on observations from a small number of monitoring points. In the second theme, we will study the system of interdependent networks, where the performance of one network depends on the performance of other networks. ******The research will enrich the toolset of dependence modeling for computer and communication networks and will benefit many real-world applications, including for example real-time multimedia delivery, performance monitoring for large-scale online broadcasting, and smart grid communication. By applying the theoretical results into our existing projects with industrial partners in Canada, our research results can benefit Canadian IT industries with more effective algorithms for data dependence analysis.