A note on large-buffer asymptotics for generalized processor sharing with Gaussian inputs

In a previous study by Dębicki and van Uitert (Queueing Syst. 54, 111–120, 2006) logarithmic large-buffer asymptotics were derived for a two-class generalized processor sharing system with Gaussian inputs, for three of the four possible scenarios. In this note we show how the large-buffer asymptotics for the remaining fourth regime follow from a recently derived result for tandem systems. We also provide a heuristic interpretation of the result. M.M. is also affiliated to CWI, P.O. Box 94079, 1090 GB Amsterdam, the Netherlands, and EURANDOM, Eindhoven, the Netherlands.