

ModelBased Estimation of Buffer Overflow Probabilities
from Measurements

Authors

Ioannis Ch. Paschalidis <yannisp@bu.edu>
Department of Manufacturing Engineering, Boston University
Spyridon Vassilaras <svassila@bu.edu>
Department of ECE, Boston University

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 Markovmodulated 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 Markovmodulated 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.

