We investigate a network routing problem where a probabilistic local broadcast transmission model is used to determine routing. We discuss this model's key features, and note that the local broadcast transmission model can be viewed as soft handoff for an ad-hoc network. We present results showing that an index policy is optimal for the routing problem. We extend the network model to allow for control of transmission type, and prove that the index nature of the optimal routing policy remains unchanged. We present three distributed algorithms which compute an optimal routing policy, discuss their convergence properties, and demonstrate their performance through simulation.