Model-based estimation of buffer overflow probabilities from measurements

Abstract

We consider the problem of estimating buffer overflow probabilities when the statistics of the input traffic are not known and have to be estimated from measurements. We start by investigating the use of Markov-modulated processes in modeling the input traffic and propose a method for selecting an optimal model based on Akaike's Information Criterion. We then consider a queue fed by such a Markov-modulated input process and use large deviations asymptotics to obtain the buffer overflow probability. The expression for this probability is affected by estimation errors in the parameters of the input model. We analyze the effect of these errors and propose a new, more robust, estimator which is less likely to underestimate the overflow probability than the estimator obtained by certainty equivalence. As such, it is appropriate in situations where the overflow probability is associated with Quality of Service (QoS) and we need to provide firm QoS guarantees. Nevertheless, as the number of observations increases, the proposed estimator converges with probability 1 to the appropriate target, and thus, does not lead to resource underutilization in this limit.