Throughput-Optimal Multi-hop Broadcast Algorithms.

In this paper we design throughput-optimal dynamic broadcast algorithms for multi-hop networks with arbitrary topologies. Most of the previous broadcast algorithms route packets along spanning trees, rooted at the source node. For large time-varying networks, computing and maintaining a set of spanning trees is not efficient, as the network-topology may change frequently. In this paper we design a class of dynamic algorithms which make packet-by-packet scheduling and routing decisions and hence, obviate the need for maintaining any global topological structures, such as spanning trees. Our algorithms may be conveniently understood as a non-trivial generalization of the familiar back-pressure algorithm, which makes unicast packet routing and scheduling decisions, based on local queue-length information and does not require to maintain end-to-end paths. However, in the broadcast setting, due to packet duplications, it is hard to define appropriate queuing structures. We design and prove the optimality of a virtual-queue based algorithm, where virtual-queues are defined for subsets of nodes. We then propose a multi-class broadcast policy which combines the above scheduling algorithm with in-class-in-order packet forwarding, resulting in significant reduction in complexity. Finally, we evaluate performance of the proposed algorithms via extensive numerical simulations.