Grant: Discovery Grants Program - Individual

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