Support: NSF grants IIS-0093581 and CCR-0330342
We want to give performance guarantees when a communication exchange takes place between two neighbors,
In particular, we want to be sure that they have been able to update their information, before their associated state reaches a variation of &delta as a consequence of their previous exchange. We are interested in finding conditions such that the probability of the agents being capable of updating their state with their neighbors within a variation of &delta is at least 1-&epsilon for some &epsilon .
In case of mobile agents, such &delta can be thought as a displacement on their respective workspace.
Thus, if we want to ensure a quality of service, constraints should be placed on the maximum speed that the agents can achieve and in the communication algorithm they are currently using (so the time between communication exchanges can be bounded) as a function of the probability of error of the communication scheme. So far, it appears to be the case that motion is so slow, that it can hide some problems that might appear in a not-very good communication system. Observe that when the velocity is assumed to be 15 m/s=54km/h (the horizontal line in both graphs) a high quality on the network can be ensured, even with a poor communication scheme and despite of the high-speed of the system.
Similarly given a particular probability of error pe, we can find the relations between &delta, &epsilon and v so we achieve a particular quality of service, which is defined by the pair ( &delta , &epsilon ).
We are also interested in finding conditions on the length of the time slot, so similar guarantees can be offered for the convergence of the synchronous average-consensus algorithm.