Multi-path Routing Metrics for Reliable Wireless Mesh Routing Topologies
  Several emerging classes of applications that run over wireless networks have a need for mathematical models and tools to systematically characterize the reliability of the network. We propose two metrics for measuring the reliability of wireless mesh routing topologies, one for flooding and one for unicast routing. The Flooding Path Probability (FPP) metric measures the end-to-end packet delivery probability when each node broadcasts a packet after hearing from all its upstream neighbors. The Unicast Retransmission Flow (URF) metric measures the end-to-end packet delivery probability when a relay node retransmits a unicast packet on its outgoing links until it receives an acknowledgement or it tries all the links. Both metrics rely on specific packet forwarding models, rather than heuristics, to derive explicit expressions of the end-to-end packet delivery probability from individual link probabilities and the underlying connectivity graph.   We also propose a distributed, greedy algorithm that uses the URF metric to construct a reliable routing topology. This algorithm constructs a Directed Acyclic Graph (DAG) from a weighted, undirected connectivity graph, where each link is weighted by its success probability. The algorithm uses a vector of decreasing reliability thresholds to coordinate when nodes can join the routing topology. Simulations demonstrate that, on average, this algorithm constructs a more reliable topology than the usual minimum hop DAG. 
Phoebus Chen, Karl H. Johansson, Paul Balister, B\'ela Bollob\'as,   Shankar Sastry
cs.NI