Modelling, Performance, and Control of Queues for Wireless Networks and Other Applications

近二十年来，随着技术的扩散，互联网的发展，无线通信的爆炸式增长，每个人的日常生活和整个社会都受到了深刻的影响。这些进展和影响极大地推动了对大规模复杂系统、多维过程、自适应模型、并行处理和计算的研究，同时也对研究所需的先进方法提出了进一步的挑战。排队理论就是这样一个例子。发展良好的经典排队理论和建模、分析、控制和优化方法不足以满足这种需求，主要是由于系统的大规模和复杂性，例如多维状态空间、系统变量的强依赖性、异构流量和非泊松行为等特性。******这项研究计划的目标是揭示模式、结构和性质，寻找新的方法，发展和扩展先进的方法，并提出有效的近似和计算程序。我们期望新的发现可以用于各种二维或高维随机系统的建模和分析，以及控制和优化，包括并行队列，串联队列和多输入，多阶段队列网络，这些网络与诸如批量到达，批量服务，耦合服务器，反馈，自适应服务和优先级等机制相结合。******当仍然期望显式性质时，对于本研究中提出的复杂系统，概率分布的显式解通常不可用。因此，近似、渐近性质、性能界限和有效的计算解成为研究的关键组成部分。提出的研究就是要解决这些问题。从核方法扩展到具有杀伤或吸收状态的随机漫步，到更一般的结构化漫步和高维模型，提出了新的发现和新的结果；推广了处理无穷多相态过程的矩阵解析方法从探索bvp的幂极限，以及显式解的参数化和代数方法；从光谱性质研究准平稳分布的衰减率应用平均域极限或平均域博弈模型进行队列最优控制通过开发高效的仿真和计算方案等，有望在排队理论、随机建模和分析方面取得进展，并对无线通信和其他应用中的系统设计、性能评估、控制和参数优化产生深远影响**

In the most recent two decades, with the proliferation of technologies, the development of the internet, and the explosion of wireless communications, everybody's daily life and society, as a whole, have been profoundly impacted. These advancements and effects have greatly motivated studies and research on large-scaled complex systems, multi-dimensional processes, adaptive models, and parallel processing and computing, while simultaneously raising further challenges on advanced methods needed in the study and research. Queueing theory is such an example. Well-developed classical queueing theory and approaches for modelling, analysis, control and optimization are not sufficient for this demand, primarily due to the large scale and complexity of the system, such as multi-dimensional state spaces, strong dependence in system variables, heterogeneous traffic, and non-Poisson behaviour, among other properties.******The objective of this proposed research program is to reveal patterns, structures and properties, search for new approaches, develop and extend advanced methods, and propose efficient approximations and computational procedures. We expect that new discoveries can be employed in both modelling and analysis, and control and optimization, for various two-or higher-dimensional stochastic systems, including parallel queues, tandem queues, and multi-input, multistage queueing networks which are incorporated with mechanisms such as bulk arrivals, bulk services, coupled servers, feedback, adaptive services, and priorities. ******When explicit properties are still expected, explicit solutions for probability distributions are not, in general, available for the complex systems proposed in this research. Therefore, approximations, asymptotics properties, performance bounds, and efficient computational solutions become key components in the study. The proposed research is to address these issues. New discoveries made and new results obtained from the proposed program, from extending the kernel method to random walks with killing or absorbing states, to more general structured walks and to high-dimensional models; from generalizing the matrix-analytic method for dealing with processes with infinitely many phase states; from exploring the limit of the power of the BVPs, and parametrization and algebraic methods for explicit solutions; from studying the decay rate in quasi-stationary distributions by spectral properties; from applying mean-fields limit, or mean-field game model for optimal control of queues; from developing efficient simulation and computational schemes and others, are expected to result in advances in queueing theory, stochastic modelling and analysis, and produce a profound impact on system design, performance evaluation, control, and parameter optimization in wireless telecommunications and other applications**