Optimal routes and flows in multicasting over ad hoc networks

We investigate optimal routing and resource allocation to maximize the system performance in multicasting over ad hoc networks. In the ad hoc environment, maximizing the network performance requires a cross-layer algorithm to determine the optimal set of routes for both multicast and unicast traffic at the network layer, the corresponding link rates and individual link transmitter powers at the data link layer and physical layer. Based on Perron Fronbenius matrix theory, we present a cross-layer approach to obtain Pareto optimal values for these system variables. By careful formulation of the multicasting path structure, we construct a network associated matrix and use its left and right eigenvectors to find this Pareto optimal operation point to maximize the network performance. We also introduces an adaptive method, direct step method (DSM), which seeks the optimal operation point iteratively.