| Dynamic scheduling of multi-class stochastic networks has wide range, as well as important, applications. Especially, today when computers and Internet, which provide plenty of important applications of stochastic networks, are reaching every corner of the world. Meanwhile, the study of these category of problems never stopped ever since they were imposed to researchers. New techniques and ideas are developed from time to time. Achievable region approaches is one of the methods employed recently, which provides not only systematic mechanism for solving particular problems, but also deep understanding of the structure of the problem.; In this thesis, we study a large class of dynamic scheduling problem, scheduling with quality of service (QoS) requirement, via achievable region approaches. The study includes the investigating of the geometric structure of the achievable regions, polymatroid, and in general, extended polymatroid, with side constraints, as well as combinatorial polynomial time algorithms for solving optimization problems over these regions. We also set up the connections between the solutions of the optimization problems and the policies that lead to optimal performance for the stochastic network. The later part of the thesis is devoted to the study of the deterministic fluid network, which is the first order approximation of the stochastic networks. |
