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We consider the problem of throughput-optimal broadcast- ing in time-varyingwireless networks, whose underlying topology is restricted to Directed AcyclicGraphs (DAG). Previous broadcast algorithms route packets along spanning trees.In large networks with time-varying connectivities, these trees are difficultto compute and maintain. In this paper we propose a new onlinethroughput-optimal broadcast algorithm which makes packet-by-packet schedulingand routing decisions, obviating the need for maintaining any globaltopological structures, such as spanning-trees. Our algorithm relies onsystem-state information for making transmission decisions and hence, may bethought of as a generalization of the well-known back-pressure algorithm whichmakes point-to-point unicast transmission decisions based on queue-lengthinformation, without requiring knowledge of end-to-end paths. Technically, theback-pressure algorithm is derived by stochastically stabilizing thenetwork-queues. However, because of packet-duplications associated withbroadcast, the work-conservation principle is violated and queuing processesare difficult to define in the broadcast problem. To address this fundamentalissue, we identify certain state-variables which behave like virtual queues inthe broadcast setting. By stochastically stabilizing these virtual queues, wedevise a throughput-optimal broadcast policy. We also derive newcharacterizations of the broadcast-capacity of time-varying wireless DAGs andderive an efficient algorithm to compute the capacity exactly under certainassumptions of interference model, and a poly-time approximation algorithm forcomputing the capacity under less restrictive assumptions.

Throughput-Optimal Broadcast in Wireless Networks with Dynamic Topology