Reduced dimension policy iteration for wireless network control via multiscale analysis

A novel framework for the analysis and optimization of wireless networks operations is proposed. The temporal evolution of the state of the network is modeled as the trajectory of the state of a Finite State Machine (FSM). The state space of the FSM and the statistics of state transition are represented as a directed graph. Graph reduction and transform techniques are proposed to reduce the dimension of the graph associated with the FSM and analyze the properties of functions defined on its state space. The proposed methodology is based on the intrinsic multi-dimensional/multi-scale structure of the state space of the FSM and enables the analysis and minimization of cost-to-go functions, i.e., functions measuring the expected long-term cost associated with a control strategy, on coarser versions of the original graph.