Throughput-Optimal Broadcast in Wireless Networks with Dynamic Topology

Abstract

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.