Complex interacting networks and systems: Models, analysis, and algorithms

复杂的系统和网络，如互联网、无线网络、云和社交网络，由大量相互作用的实体（用户和资源）组成，这些实体以随机的方式相互作用，决定了它们的功能和整个系统的宏观行为。为了管理网络和系统的复杂性，我们需要了解它们的动态和紧急行为，以便设计稳定、高效和安全运行的算法，并提供用户体验。今天的系统在规模上有很大的不同，基本的问题不仅仅是交通问题。因此，所需的方法非常不同，超出了传统的排队模型、优化和资源分配。由于系统在用户、资源和空间分布方面都很大，我们需要了解局部与全局行为的问题，以及不需要太多信息的分布式算法的设计。研究的目的是了解异质性的影响，资源的大小和人口，以及如何使用这些来表征性能。

Complex systems and networks such as the internet, wireless networks, the cloud, and social networks, are comprised of large numbers of interacting entities (users and resources) that interact in a random way that determine their functionality and the macroscopic behavior of the overall system. To manage the complexity of networks and systems we need to understand their dynamic as well as emergent behavior in order to design algorithms for their stable, efficient, and secure operation as well as for providing user experience. The systems of today are vastly different in scale and the basic issues are not simply traffic issues. The methodologies required are therefore very different that go beyond classical queueing models, optimization,  and  resource allocation. Since the systems are large in terms of users, resources, and are spatially distributed we need to understand the issues of local vs. global behavior and the design of distributed algorithms that do not require too much information. The research will aim at understanding the impact of heterogeneity and the size and population of resources and how these can be used to characterize the performance. The  research will concern itself with the issues of complexity and the stochastic behavior of such networks and systems. The aim is to address the main problems that impact stability and performance. The goal is the design of  simple efficient and distributed algorithms for user experience and system efficiency. The techniques will draw upon stochastic networks, generalized voter models, mean field or McKean-Vlasov analysis, randomized algorithms, random graphs especially the spectral theory, and bandit processes. The research will be pursued with the following principal application thrusts: 1) Wireless networks, 2) Social networks and security, 3) Network performance and algorithms , and 4) Cloud computing and applications.  The aim is to study the interplay between size and emergent behavior, while using averaging to devise  simple algorithms for resource optimization and providing predictable performance to both users and operators. In each of the constituent application areas the research contributions will be in models, their analysis with performance being the focus, and the design of distributed and randomized algorithms for scalability without sacrificing efficiency. The aim is to develop the theoretical frameworks necessary for the design of robust and stable algorithms that will allow resource allocation and optimization. A key component is the training research students to acquire wider variety of tools and techniques that are necessary to deal with the new problems that are not part of classical training which will lead to new courses and monographs. The research likely to enrich the constituent fields from where the tools will be drawn namely stochastic networks, bandit processes, randomized algorithms and graphical models.