Stochastic optimization and its applications in time- varying wireless systems

With the advent of third generation wireless cellular systems, new functionalities are deployed to support dynamic adjustments of system parameters and operating points. How to effectively manage the resources using these functions with system state information, such like queue dynamics, packet delay and channel fluctuation, is very critical to the system performance. greatly increase the chance of encountering better channel states, and helps in achieving better average resource utilization. In this dissertation, we investigate the optimal channel- aware scheduling policy for applications concerned with the long-term average performance (such as average power consumption and throughput, etc.), and the realization of the policy in various contexts. A broad class of scheduler design problems can be expressed as optimal stochastic control problems concerned with the time and ensemble average of controlled processes. In light of this, we devise a framework for stochastic dynamic control utilizing a mathematical tool, referred to as Stochastic Optimization. Leveraging the duality approach developed for convex optimization, we simplify the constrained Stochastic Optimization problem into an unconstraint one. Furthermore, we develop an online algorithm for solving the stochastic optimization problem. For a broad class of stationary stochastic processes which satisfy a set of mixing conditions, the behavior of the algorithm can be approximately characterized by a projected differential inclusion. Exploring the trajectory of the projected differential inclusion, it is proved that the long-term average of the control variables generated by the proposed algorithm along its recursive steps converges asymptotically to the optimal one. To demonstrate the use cases of the established framework, we study the power- optimized routing problem in multi-hop wireless networks. A distributed implementation of the algorithm is devised. Applying the same framework, we also look into the problem of joint source distortion management and wireless downlink scheduling, in which we aim to minimize the maximum average distortion of the data requested by each user. The proposed algorithm comes with the properties of finite receiver buffer occupation as well as the negligible packet-drop rati