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.

Optimal design of measurements on queueing systems

“…As in this case measuring a queue interferes with it, we need to allow time for the queue to return to its stationary distribution before measuring again. We saw a similar result for observing Markov chains in [31] and [32].…”

“…In [31] the discrete time two parameter birth death process is studied, and this is generalised in [32] for general Markov chains. For a wide class of Markov chains, with a discrete state space and transitions at discrete times, optimal times for measurements are found.…”

Simultaneous estimation of state and packet-loss occurrences in networked control systems

“…If the data packet transmissions in different communication links are not simultaneous or the communication mediums are separated, then α i,k for i ∈ {1..r} are independent binary-valued random variables. As a result, the transition probabilities in (6) can be computed easily in terms of the indivdual packet loss probabilities that are much easier to be obtained empirically [26]. It is also mentioned that, in some cases the packet loss probabilities are computable based on theoretical analysis of the underlying communication network [27,28].…”