Reliable Broadcast in a Wireless Grid Network with Probabilistic Failures

We consider a wireless grid network in which nodes are prone to failure. In the considered failure mode, each node has an independent probability of failure p, and failures may be either Byzantine or crash-stop in nature. All nodes are assumed to have a common transmission range r, and a resultant common degree d. We establish necessary and sufficient conditions for the degree of each node as a function of the total network size n and the failure probability p, so as to ensure that reliable broadcast succeeds with probability 1, as n → ∞. Our results indicate that reliable broadcast is asymptotically achievable with Byzantine failures if p < 1 2 , and the degree of each node is Θ ( lnn ln 1 2p +ln 1 2(1−p) ) . These results exhibit similarity of form to results obtained for crash-stop failures that indicate a required degree of Θ (

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