Asymptotic analysis of GPS systems fed by heterogeneous long-tailed sources

In this paper we consider a multi-buffered system consisting of N buffers accessed by heterogeneous long-tailed sessions and served according to the generalized processor sharing (GPS) discipline with weights {/spl phi//sub i/}. We assume that sessions arrive according to a Poisson process. A session of type i transmits at rate r/sub i/ and has a duration whose distribution is longtailed of the form P(/spl tau//sub i/>t)/spl sim//spl alpha//sub i/t/sup -(1+/spl beta/i)/ where /spl alpha//sub i/, /spl beta//sub i/>0. We obtain the large buffer asymptotics under very general stability hypotheses. In particular we show that recent results on the GPS asymptotics obtained by Borst, Boxma and Jelenkovic (see IEEE INFOCOM, vol.2, p.912-21, 2000) can be recovered and there are important cases for which we obtain exact asymptotes for which the previous results do not apply. The methodology exploits the sample-path description of the workload evolution under GPS as well as the marked Poisson structure of the inputs.