Throughput-Optimal Broadcast in Wireless Networks with Dynamic Topology

We consider the problem of throughput-optimal broadcasting in a time-varying wireless network with an underlying Directed Acyclic (DAG) topology. Known broadcast algorithms route packets along pre-computed spanning trees. In large wireless networks with time-varying connectivities, the optimal trees are difficult to compute and maintain. In this paper, we propose a new online throughput-optimal broadcast algorithm, which takes packet-by-packet scheduling and routing decisions, obviating the need for any global topological structures, such as spanning trees. Our algorithm utilizes certain queue-like system-state information for making transmission decisions and hence, may be thought of as a generalization of the well-known back-pressure policy, which makes point-to-point unicast transmission decisions based on the local queue-length information. Technically, the back-pressure algorithm is derived by greedily stabilizing the queues. However, because of packet-duplications, the work-conservation principle is violated, and an analogous queueing process is non-trivial to define in the broadcast setting. To address this fundamental issue, we identify certain state variables whose dynamics behave like virtual queues. By stochastically stabilizing these virtual queues, we devise a throughput-optimal broadcast policy. We also derive new characterizations of the broadcast capacity of time-varying wireless DAGs and propose efficient algorithms to compute the capacity either exactly or approximately under various assumptions.