Exact solutions for a generalized two-demand queueing model

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，推动了对复杂系统的学习和研究， 多维过程、自适应模型以及并行处理和计算。发展良好 在这一研究领域中，随机建模和分析中的经典排队理论和方法是不够的，这主要是由于系统的复杂性、多维状态空间、系统变量中存在的强相关性、异质的Qos业务和非泊松行为等特性。 提出的研究计划的目标是加深我们对性质的理解，揭示模式和结构，寻找新的途径，开发先进的方法，提出有效的计算程序，并提出良好的近似。与简单系统不同的是，经典排队方法对于显式解往往是有效的，而需要新的概念和方法来处理复杂的多维系统。随机建模、逼近、渐近性质、性能界和有效的计算解成为研究多维系统的关键组成部分。建议的研究旨在使用、推广和进一步发展各种先进的方法和途径。 我们期待所提出的研究将带来新的发现，填补数学理论基础研究，特别是概率和随机过程与工程应用之间的空白，并在高级排队理论方面取得新的进展。这些新的研究成果将为工程设计人员提供无线通信网络和计算机网络的设计、建模、分析和优化的原理和定理，并在研究领域产生深远的影响。

Technological advances in the Internet and wireless networks and the integration between them have profoundly impacted everybody's daily life and have motivated studies and research on complex systems, multi-dimensional processes, adaptive models, and parallel processing and computing. Well-developed classical queueing theory and approaches in stochastic modelling and analysis are not sufficient within this area of study, largely due to the complexity of the system, multi-dimensional state space, strong dependence presented in system variables, heterogeneous QoS traffic, and non-Poisson behaviour among other properties. The objective of the proposed research program is to deepen our understanding of properties, reveal patterns and structures, search for new approaches, develop advanced methods, propose efficient computational procedures, and put forward good approximations. Unlike for simple systems, for which classical queueing methods are often effective for explicit solutions, new concepts and approaches are required to tackle complex multi-dimensional systems. Stochastic modelling, approximations, asymptotic properties, performance bounds, and efficient computational solutions become key components in the study of multi-dimensional systems. The proposed research aims to use, extend, and further develop various advanced methods and approaches. We expect that the proposed research will lead to new discoveries that will fill gaps between theoretical fundamental studies in mathematics, especially in probability and stochastic processes and engineering applications, and make new advances in advanced queueing theory. The new research results obtained will be significant in providing engineering designers with principles and theorems in design, modelling, analysis and optimization of wireless communication networks and computer networks and to produce a profound impact in the area of research.