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

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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.

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Authors and Affiliations

  1. CWI, P.O. Box 94079, 1090 GB, Amsterdam, The Netherlands

    Sem Borst & Onno Boxma

  2. Department of Mathematics & Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Sem Borst & Onno Boxma

  3. Bell Laboratories, Lucent Technologies, P.O. Box 636, Murray Hill, NJ, 07974, USA

    Sem Borst

  4. Department of Electrical Engineering, Columbia University, New York, NY, 10027, USA

    Predrag Jelenković

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  2. Onno Boxma
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  3. Predrag Jelenković
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Borst, S., Boxma, O. & Jelenković, P. Reduced-Load Equivalence and Induced Burstiness in GPS Queues with Long-Tailed Traffic Flows. Queueing Systems 43, 273–306 (2003). https://doi.org/10.1023/A:1023237129453

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