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

近年来，技术的激增，大数据的更容易获取，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的指数级增长，深刻地影响了每个人的日常生活。这些进展及其随之而来的影响带来了许多新的挑战，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。许多新的挑战不能通过经典或标准方法令人满意地解决，这些方法需要新的创新的数学/统计建模和解决方法。排队论就是这样一个例子。成熟的经典排队理论及其方法不足以应对这些现代挑战。这种不足的主要原因是系统的规模和复杂性，如多维状态空间、对系统变量的强烈依赖、异质流量、非泊松行为或关于系统的不完全信息。这项拟议的研究计划的主要目标是解决上述挑战的基本问题。它的目标是开发或扩展高级建模工具，发现或揭示结构性质，证明定理，填补理论研究和应用之间的空白，并为决策提供有效的近似、计算或模拟和推理。一般情况下，显式解不适用于本研究中提出的复杂系统。因此，近似、渐近性质、性能界以及有效的模拟算法、计算解或统计推断成为研究的关键部分。我们期望这项研究将在推进排队论、随机建模与分析、性能评估、决策、应用概率和运筹学等领域的知识方面做出原创性和重大的贡献。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、卫生、商业和金融、社会服务系统，以及可能还有更多领域。我们建设性的HQP培训计划，包括促进从代表性不足的群体中招聘更多HQP和改善培训环境，将使受过培训的HQP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.