Modelling, Performance, and Decision Making of Queues for Wireless Networks and Beyond

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In recent years, the proliferation of technologies, easier access to big data, wide introduction of cloud storage and computing, and exponential growth of the Internet, wireless and smartphone apps have profoundly impacted everybody's daily life. These advancements and their subsequent impacts have created many new challenges, which in turn greatly motivate research on large-scale complex systems, multi-dimensional networks, adaptive models, parallel processing, and cloud computing. Many of the new challenges cannot be satisfactorily addressed by classical or standard methods, which call for new innovative mathematical/statistical modeling and solution methodologies. Queueing theory is such an example. Well-developed classical queueing theory and its approaches are not sufficient to meet these modern challenges. This insufficiency results primarily from the large scale and complexity of the system, such as multi-dimensional state spaces, strong dependence in system variables, heterogeneous traffic, non-Poisson behaviour, or incomplete information about the system. The main objective of this proposed research program is to address fundamental issues for the above-mentioned challenges. It aims to develop or extend advanced modeling tools, discover or reveal structure properties, prove theorems, fill the gap between theoretical research and applications, and propose efficient approximations, computations or simulation, and inferences for decision-making. Explicit solutions are not, in general, available for the complex systems proposed in this research. Therefore, approximations, asymptotic properties, performance bounds, and efficient simulation algorithms, computational solutions or statistical inference become key components in the study. We expect that original and significant contributions will be made for the proposed research, in advancing knowledge in the fields of queueing theory, stochastic modelling and analysis, performance evaluation, decision-making, applied probability and operations research. The far-reaching applications of these topics will extend to computer management, telecommunication systems, transportation, manufacturing, health, business and finance, social service systems, and possibly many more. Our constructive HQP training plan, including promotions to recruit more HQP from under-represented groups and improvement of the training environment, will better prepare the trained HQP for future career challenges and making their significant contributions to Canadian economy and society.