Queueing Models and Performance Analysis -- Telecommunication Systems and Other Applications

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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, for various multi-dimensional stochastic systems, including multiple waiting lines queues, tandem queues, and other queueing models which are incorporated with mechanisms such as bulk queues, coupled servers, adaptive services, and priorities. These stochastic systems offer new challenges, as outlined above, and through our development of proposed advanced methods in dealing with these challenges, we aim at providing solutions to engineering and computer problems and other queueing applications.***When explicit properties are expected, explicit solutions for probability distributions are not, in general, available for the complex systems proposed in this research. Therefore, approximations, asymptotic properties, performance bounds, become key components in the study. The proposed research is to use, extend, and further develop the following methodology and approaches: the kernel method for asymptotics; boundary-value problems (BVP) approach and analytic (uniformization / algebraic) method for explicit solutions; the matrix analytic method (MAM) for processes with infinitely many phase states, among others.******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 uniformization and algebraic methods for explicit solutions; from studying the decay rate in quasi-stationary distributions by spectral properties, are expected to be original and significant results in advances in queueing theory, stochastic modelling and analysis, and produce profound impact on system design and performance evaluation, telecommunication systems and other applications.**