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

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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.