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Generalized processor sharing queues with heterogeneous traffic classes

Part of: Special processes Operations research and management science Computer system organization

Published online by Cambridge University Press:  01 July 2016

Sem Borst ,
Michel Mandjes  and
Miranda van Uitert
Sem Borst*
Affiliation:
CWI, Amsterdam, Bell Laboratories Lucent Technologies and Eindhoven University of Technology
Michel Mandjes*
Affiliation:
CWI, Amsterdam, Bell Laboratories Lucent Technologies and University of Twente
Miranda van Uitert*
Affiliation:
CWI, Amsterdam
*
∗ Postal address: CWI, PO Box 94079, 1090 GB Amsterdam, The Netherlands.
∗ Postal address: CWI, PO Box 94079, 1090 GB Amsterdam, The Netherlands.
∗ Postal address: CWI, PO Box 94079, 1090 GB Amsterdam, The Netherlands.
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Abstract

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 behaviour 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 by a certain prefactor, which accounts for the interaction with the heavy-tailed flow. Specifically, the prefactor 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.

Keywords

Fluid queuegeneralized processor sharing (GPS)heavy-tailed trafficlarge deviationqueue length asymptoticsregular variationweighted fair queueing (WFQ)

MSC classification

Primary: 60K25: Queueing theory
Secondary: 68M20: Performance evaluation; queueing; scheduling 90B18: Communication networks 90B22: Queues and service
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 35 , Issue 3 , September 2003 , pp. 806 - 845
Copyright
Copyright © Applied Probability Trust 2003 

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