This article is cited in 2 papers

Papers to the reports presented at the XXIX International Seminar on Stability Problems for Stochastic Models (Svetlogorsk Kaliningrad region, Russia, 10–16 October 2011)

Asymptotics of the maximum workload for a class of gaussian queueing systems

O. V. Lukashenko^ab, E. V. Morozov<sup>ba

a</sup> Institute of Applied Mathematical Research, Karelian Research Centre, RAS, Petrozavodsk
^b Petrozavodsk State University

Abstract: The asymptotics of the maximum workload in a fluid queueing system fed by a process containing a random component are described by a centered Gaussian process. It is assumed that the variance of the process is a regularly varying at infinity function with index belonging to interval $(0,2)$. Such class of processes includes, in particular, a sum of independent fractional Brownian motions. It is shown that, under an appropriate scaling, the maximum workload over interval $[0,t]$ converges in probability to an explicitly given constant as $t$ increases.

Keywords: Gaussian queueing system; maximum workload; fractional Brownian motion; asymptotical analysis; regular variation.