Delivery Delay and Mobile Faults

In this work we address the problem of reaching approximate consensus in a complete network of $n$ nodes, where message deliveries can be delayed by at most $d$ time-steps. We consider a mobile adversary, which corrupts at most $f$ nodes in any step, modeled as a synchronous round. We explicitly study how $d$ affects the feasibility of the problem. More precisely, we propose a framework to analyze mobile fault-tolerance in the presence of message delays. We prove that approximate consensus is feasible if and only if $n$ > 4df. We assume no knowledge of time (round index) by the nodes; instead, in our model, whenever a message is sent, it is timestamped by the communication channel. We propose the tight TimeStamps algorithm, which utilizes timestamps to optimally bound the number of faulty messages.