Tail-Limited Phase-Type Burstiness Bounds for Network Traffic

Massieh Kordi Boroujeny, Brian L. Mark, Yariv Ephraim

Abstract: The bursty nature of network traffic makes it difficult to characterize accurately, and may give rise to heavy-tailed queue distributions within the network. Building on prior work in stochastic network calculus, we propose traffic burstiness bounds based on the class of phase-type distributions and develop an approach to estimate the parameter of such bounds using the expectation-maximization (EM) algorithm. By limiting the tail of the burstiness bound, our approach achieves a better fit of the phase-type distribution to the empirical data from heavy-tailed traffic. The proposed tail-limited phase-type burstiness bounds fall within the framework for stochastic network calculus based on generalized stochastically bounded burstiness. We demonstrate the effectiveness of the proposed methodology with a numerical example involving a heavy-tailed M/G/1 queue.