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.
Keywords Generalized processor sharing - Fractional Brownian motion
Mathematics Subject Classification (2000) 60K25 - 68M20
K.D. was supported by KBN Grant No. 1 P03A 031 28 (2005–2007).
M.M. is also affiliated to CWI, P.O. Box 94079, 1090 GB Amsterdam, the Netherlands, and EURANDOM, Eindhoven, the Netherlands.