Fitting Network Traffic to Phase-Type Bounds

Network traffic is difficult to characterize due to its random, bursty nature. Even if a traffic source could be fit to a stochastic model with reasonable accuracy, analysis of end-to-end network performance metrics for such traffic models is generally intractable. In prior work, an approach to characterize traffic burstiness using a bound based on the class of phase-type distributions was proposed. Such phase-type bounds could be applied in conjunction with stochastic network calculus to derive probabilistic end-to-end delay bounds for a traffic stream. In this paper, we focus on the problem of estimating a tight phase-type burstiness bound for a given traffic trace. We investigate a method based on least squares and another based on the expectation-maximization algorithm. Our numerical results compare the two approaches in the scenario of a heavy-tailed M/G/1 queue. We find that while both methods are viable approaches for deriving phase-type bounds on traffic burstiness, the least squares approach performs better, particularly when a tail limit is imposed.1