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

在最近的二十年里，随着技术的激增、互联网的发展和无线通信的爆炸性增长，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、自适应模型以及并行处理和计算的学习和研究，同时也对学习和研究所需的先进方法提出了进一步的挑战。排队论就是这样一个例子。由于系统的规模和复杂性，如多维状态空间、对系统变量的强依赖性、异质流量和非泊松行为等特性，传统的排队论和建模、分析、控制和优化方法已不能满足这一需求。我们期待新的发现可以用于各种二维或更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、多级排队网络，这些网络结合了成批到达、成批服务、耦合服务器、反馈、自适应服务和优先级等机制。*当仍然期望显式性质时，概率分布的显式解一般不适用于本研究中提出的复杂系统。因此，近似、渐近性质、性能界和有效的计算解成为研究的关键部分。拟议的研究就是为了解决这些问题。从核方法扩展到具有杀死或吸收状态的随机游动，到更一般的结构游动和高维模型，从推广矩阵分析方法处理具有无限多个相态的过程，从探索BVPS的功率极限，到显式解的参数化和代数方法，从根据谱性质研究准平稳分布的衰减率，从应用平均场极限或平均场博弈模型到队列的最优控制，从扩展核方法到具有杀死或吸收状态的随机游动，到推广到高维模型，从推广矩阵分析方法到处理无限多个相态过程的矩阵分析方法，从探索BVPS的功率极限，到显式解的参数化和代数方法，从根据谱性质研究准平稳分布的衰减率，从应用平均场极限或平均场博弈模型，到应用平均场极限或平均场博弈模型；通过开发高效的模拟和计算方案等，有望推动排队论、随机建模和分析的进步，并对无线电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**