Design of Experiments for Categorical Repeated Measurements in Packet Communication Networks

Abstract

We study the optimal measurement of packet loss and delay in packet networks by treating all measurements as numerical experiments to which we apply the theory of the design of experiments. Specifically we seek to find the optimal times at which to inject survey (probe) packets. Our approach is to model the target node in the packet communication network, an access buffer, as a discrete-time Markov chain. Given that we may only make a limited number of observations, we present a method for optimally designing the observation times for the chain, and derive both exact and continuous optimal designs. Our results show that, for common optimality criteria, measuring at a uniform rate may not be optimal. This has significance for influencing commercial practice as uniform probing is standard. We show how our method may be generalized to Markov systems with larger state space, and describe computational methods to find optimal designs on any system which evolves according to the Markov principle.