On an estimation oriented routing protocol

Consider the problem of estimation of a linear time-invariant process across a communication channel such that the sensor data is delayed by a stochastic time-varying delay that can potentially be infinite. Thus, the data may arrive at the receiver delayed and out of order, or may simply be lost. There are two main contributions of this work. We show that performance of the estimator can not be characterized through a few moments of the delay distribution. Thus, conjectures such as a delay distribution with lesser mean or lesser maximum value always yields better estimation performance are incorrect. For a graph with each edge introducing a random delay to the sensor data, we also provide a routing algorithm that searches for the path that is optimal from an estimation theoretic perspective. A minor contribution of the work is to prove that even if the delay distribution has an infinite support and the delays are correlated across time with a finite memory, the necessary and sufficient condition for stability depends merely on the erasure probability.