We consider a queue fed by a mixture of light-tailed and heavy-tailed traffic. The two traffic flows are served in accordance with the Generalized Processor Sharing (GPS) discipline. GPS-based scheduling algorithms, such as Weighted Fair Queueing (WFQ), have emerged as an important mechanism for achieving service differentiation in integrated networks. We derive the asymptotic workload behavior of the light-tailed traffic flow under the assumption that its GPS weight is larger than its traffic intensity. The GPS mechanism ensures that the workload is bounded above by that in an isolated system with the light-tailed flow served in isolation at a constant rate equal to its GPS weight. We show that the workload distribution is in fact asymptotically equivalent to that in the isolated system, multiplied with a certain pre-factor, which accounts for the interaction with the heavy-tailed flow. Specifically, the pre-factor represents the probability that the heavy-tailed flow is backlogged long enough for the light-tailed flow to reach overflow. The results provide crucial qualitative insight in the typical overflow scenario.

Queueing theory (msc 60K25), Performance evaluation; queueing; scheduling (msc 68M20), Communication networks (msc 90B18), Queues and service (msc 90B22)
Logistics (theme 3), Energy (theme 4)
CWI. Probability, Networks and Algorithms [PNA]

Borst, S.C, Mandjes, M.R.H, & van Uitert, M.J.G. (2001). Generalized processor sharing queues with heterogenous traffic classes. CWI. Probability, Networks and Algorithms [PNA]. CWI.