Exact solutions for a generalized two-demand queueing model

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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.