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研究和研究。由于系统的复杂性、多维状态空间、系统变量的强依赖性或相互作用、异构流量、非泊松行为等特性，在随机建模和分析中发展良好的经典混沌理论和方法不足以用于本研究。这项研究计划的目的是发现新的方法，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，多级排队网络，这些网络与诸如批量到达，批量服务，耦合服务器，反馈，自适应服务等机制相关，这些机制受到电信技术进步的推动，以满足上述新的挑战，并提供工程问题的解决方案。近似，渐近性质，性能界限和有效的计算解决方案是在研究中的关键组成部分。本研究将使用、扩展和进一步发展以下方法和途径：无穷多相态过程的矩阵分析方法;谱性质;截尾概念; RG-因子分解;马尔可夫更新理论;马尔可夫加性过程;奇异性分析。这些新的发现和结果将对通信系统的设计、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.