Joint stochastic routing and scheduling for multihop wireless ad-hoc networks

We consider the problem of finding multihop routes in a wireless ad-hoc network jointly with scheduling transmission times of different information flows. Taking into account the unreliable nature of wireless channels, we derive a joint stochastic routing-scheduling algorithm whereby schedules and routes are selected at random with certain probabilities that we optimize. We prove that if there exists a set of (random) schedules and routes ensuring that all queues in the network are stable, our protocol converges to one such set. Our approach to the problem is to: i) characterize the set of scheduling - routing policies guaranteeing that all queues in the network are stable; ii) show that this can be reduced to finding a set of auxiliary variables in a convex polyhedron; and iii) use dual decomposition techniques to develop an algorithm converging to a point inside this convex polyhedron.