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

近年来，技术的激增，更容易获得大数据，云存储和计算的广泛引入，以及互联网，无线和智能手机应用程序的指数增长，深刻影响了每个人的日常生活。这些进步及其后续影响带来了许多新的挑战，这反过来又极大地推动了对大规模复杂系统，多维网络，自适应模型，并行处理和云计算的研究。许多新的挑战不能令人满意地解决经典或标准的方法，这需要新的创新的数学/统计建模和解决方案的方法。进化论就是这样一个例子。发达的经典理论及其方法已不足以应对这些现代挑战。这种不足主要是由于系统的大规模和复杂性，如多维状态空间，系统变量的强依赖性，异构流量，非泊松行为，或不完整的信息系统。这项拟议研究计划的主要目标是解决上述挑战的基本问题。它旨在开发或扩展先进的建模工具，发现或揭示结构特性，证明定理，填补理论研究和应用之间的差距，并提出有效的近似，计算或模拟，以及决策推理。 显式的解决方案，在一般情况下，可用于本研究中提出的复杂系统。因此，近似，渐近性质，性能界限，有效的模拟算法，计算解决方案或统计推断成为研究的关键组成部分。 我们期望，原始的和重大的贡献，将提出的研究，在推进知识领域的嵌入理论，随机建模和分析，性能评估，决策，应用概率和运筹学。这些主题的深远应用将扩展到计算机管理，电信系统，运输，制造，健康，商业和金融，社会服务系统，可能还有更多。我们建设性的HQP培训计划，包括从代表性不足的群体中招募更多的HQP和改善培训环境，将更好地为未来的职业挑战做好准备，并为加拿大经济和社会做出重大贡献。

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.