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Queueing Systems

, Volume 43, Issue 4, pp 273–306 | Cite as

Reduced-Load Equivalence and Induced Burstiness in GPS Queues with Long-Tailed Traffic Flows

  • Sem Borst
  • Onno Boxma
  • Predrag Jelenković
Article

Abstract

We analyze the queueing behavior of long-tailed traffic flows under the Generalized Processor Sharing (GPS) discipline. We show a sharp dichotomy in qualitative behavior, depending on the relative values of the weight parameters. For certain weight combinations, an individual flow with long-tailed traffic characteristics is effectively served at a constant rate. The effective service rate may be interpreted as the maximum average traffic rate for the flow to be stable, which is only influenced by the traffic characteristics of the other flows through their average rates. In particular, the flow is essentially immune from excessive activity of flows with ‘heavier’-tailed traffic characteristics. In many situations, the effective service rate is simply the link rate reduced by the aggregate average rate of the other flows. This confirms that GPS-based scheduling algorithms provide a potential mechanism for extracting significant multiplexing gains, while isolating individual flows. For other weight combinations however, a flow may be strongly affected by the activity of ‘heavier’-tailed flows, and may inherit their traffic characteristics, causing induced burstiness. The stark contrast in qualitative behavior illustrates the crucial importance of the weight parameters.

Generalized Processor Sharing induced burstiness long-tailed traffic reduced-load equivalence Weighted Fair Queueing workload asymptotics 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Sem Borst
    • 1
    • 2
    • 3
  • Onno Boxma
    • 1
    • 2
  • Predrag Jelenković
    • 4
  1. 1.CWIAmsterdamThe Netherlands
  2. 2.Department of Mathematics & Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands
  3. 3.Bell LaboratoriesLucent TechnologiesMurray HillUSA
  4. 4.Department of Electrical EngineeringColumbia UniversityNew YorkUSA

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