Reducing packet loss bursts in a wireless mesh network for stochastic bounds on estimation error

A big challenge for wireless networked control systems is how to design the underlying networking algorithms and protocols to provide high reliability, defined as the end-to-end probability of packet delivery, despite the high packet loss rates of individual wireless links. This paper formulates the problem of jointly designing a set of packet forwarding policies on a multipath mesh network to meet control application requirements. We derive several results to help understand the problem space. First, we demonstrate that some common approaches, like applying a single forwarding policy to all packets or always routing packets on disjoint paths, are not optimal for the application when the links are bursty. Second, we introduce the notion of dominance to give a partial ordering to sets of forwarding policies, used to prove that an optimal policy schedules all outgoing links at each node and that an upper bound on the performance attained by unicast forwarding policies on the network graph can be computed assuming a flooding policy. Third, we demonstrate how to convert application performance metrics to packet forwarding policy objectives, using the probability that the error covariance of a Kalman filter stays within a bound as our application metric. Fourth, we provide an algorithm to compute the joint probability mass function that a sequence of packets are delivered, given a set of policies and a network graph. Finally, we describe how to obtain optimal policies via an exhaustive search, motivating future research for more computationally efficient solutions.