Time to buffer overflow in an MMPP queue

Abstract

In this report we deal with the time to buffer overflow in a finite-buffer queue with MMPP (Markov-modulated Poisson process) arrivals. The results include a closed-form formula for the transform of the distribution of the time to buffer overflow. The main benefit of this formula is that, using properties of the transform, we can easily compute the average overflow time and all the moments (variance etc). Moreover, by means of an inversion algorithm, we can obtain the probability density function and cumulative distribution function of the overflow time. Analytical results are illustrated by a numerical example based on MMPP parameterization fitted to an IP traffic trace file. © IFIP International Federation for Information Processing 2007.