A Calculus Approach for Stochastic Networks: From Communication Networks to Smart Grids to Internet Water Army

不确定性在现实世界的网络系统中无处不在。例如，在计算机和通信网络中，数据流量与最终用户的行为和流行的社会事件高度耦合，两者并不总是确定性的；在现代电网中，分布式可再生能源(如风能和太阳能)对减少二氧化碳排放至关重要，但可再生能源通常具有不确定性，其可用性很难预测；在在线社交网络中，人们经常以概率的方式相互作用或关注社会事件。在所有这些网络系统中，了解不确定性是更好地控制系统的基础。特别是，回答以下问题至关重要：如何对不确定性进行建模？不确定性对网络性能有何影响？在输入不确定的情况下，如何对系统进行控制？本研究建议用随机网络演算(SNC)来解决上述基本问题，SNC是一个活跃但仍处于萌芽状态的研究领域。 由于SNC的发展历史较短，缺乏处理SNC所涉及的密集计算的快速算法，目前的SNC理论还不成熟，在实际应用中也没有看到太多的成功。这项研究的目的是推动SNC的边界，使其易于访问，并广泛适用于广泛的实际问题。通过数学分析、仿真和真实世界实验，该项目将解决SNC发展过程中交织在一起的三个研究主题：性能建模和评估、最优随机控制和高效数值计算。 这项研究将丰富随机建模和随机控制的工具包，并将有益于计算机与通信网络、在线社会网络和电力网络等许多科学和工程领域。通过将理论结果应用于我们在加拿大的现有工业项目，如微型智能电网的电力可靠性和分布式智能照明控制，我们希望对随机网络系统进行更有效的控制，并在加拿大的IT和能源行业节省大量成本。

Uncertainty is ubiquitous in real-world network systems. For example, in computer and communication networks, data traffic is highly coupled with end users' behavior and popular social events, both of which are not always deterministic; in modern power grids, distributed renewable energy sources (e.g., wind and solar energy) are important to reduce carbon dioxide emission, but renewable energy sources are normally uncertain, and their availability is hard to predict; in online social networks, people often interact with each other or follow social events in a probabilistic fashion. In all these network systems, it is fundamental to understand the uncertainty for better system control. In particular, it is critical to answer the following questions: How to model the uncertainty? What is the impact of uncertainty on the network performance? How to control the system in the presence of uncertain input? This research proposal addresses the above fundamental questions with Stochastic Network Calculus (SNC), an active yet still-nascent research field. Due to its short history and the lack of fast algorithms to handle the intensive computation involved in SNC, current SNC theory is still immature and has not seen many successes in practical applications. The objective of this research is to push the boundary of SNC and make it easily accessible and broadly applicable to a large range of practical problems. With mathematical analysis, simulation, and real-world experiments, the project will address three interweaving research themes in the development of SNC: performance modeling and evaluation, optimal stochastic control, and efficient numerical calculation. The research will enrich the toolset of stochastic modeling and stochastic control and will benefit many scientific and engineering areas, such as computer and communication networks, online social networks, and electric power networks. By applying the theoretical results into our existing industrial projects in Canada, such as power reliability of micro smart grids and distributed intelligent lighting control, we expect more effective control on stochastic network systems and high cost saving in Canadian IT and energy industries.