Stochastic modeling and performance analysis for systems and networks in telecommunications

互联网和无线网络的技术进步以及它们之间的融合深刻地影响了每个人的日常生活，并推动了对复杂系统的学习和研究。由于系统的复杂性、多维状态空间、系统变量的强相关性或强相互作用、异质流量、非泊松行为等特性，传统的随机建模和分析中的经典排队理论和方法不足以满足本研究和研究的需要。这项拟议的研究计划的目标是发现新的方法，开发先进的方法，并提出有效的计算程序。我们期望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，包括并行队列、串联队列和多输入多阶段排队网络，这些网络在电信技术进步的推动下，与诸如成批到达、成批服务、耦合服务、反馈、自适应服务等机制相结合，以应对上述新的挑战并为工程问题提供解决方案。近似、渐近性质、性能界和有效的计算解是研究的关键部分。这项研究将使用、推广和进一步发展以下方法论和方法：无穷多个相态过程的矩阵分析方法；谱性质；截尾概念；RG分解；马尔可夫更新理论；马尔可夫可加过程；奇异性分析。我们预计，新的发现和结果将对电信系统设计、性能评估和参数优化产生深远的影响。

Technology advances in the Internet and wireless networks, and the integration between them have profoundly impacted everybody's daily life and motivated studies and research on complex systems. Well-developed classical queueing theory and approaches in stochastic modelling and analysis are not sufficient for this study and research, largely due to the complexity of the system, multi-dimensional state space, strong dependence or interaction in system variables, heterogeneous traffic, non-Poisson behaviour among other properties. The objective of this proposed research program is to discover new approaches, develop advanced methods, and propose efficient computational procedures. We expect that new discoveries can be employed in modelling and analysis for various two- or higher-dimensional stochastic systems, including parallel queues, tandem queues, and multi-input, multistage queueing networks incoorporated with mechanisms such as bulk arrivals, bulk services, coupled servers, feedback, adaptive services, and possible others, motivated by technology advances in telecommunications, to meet new challenges outlined above and provide solutions to engineering problems. Approximations, asymptotics properties, performance bounds, and efficient computational solutions are the key components in the study. The proposed research is to use, extend, and further develep the following methodology and approaches: the matrix-analytic method for processes with infinitely many phase states; spectral properties; the concept of censoring; the RG-factorization; Markov renewal theory; Markov additive processes; sigularity analysis. We expect that new discoveries and results would produce profund impact on system design, performance evaluation and parameter optimization in telecommunications.