Tail asymptotics for discriminatory processor-sharing queues with heavy-tailed service requirements

  • Authors:

  • Sem Borst;Dennis van Ooteghem;Bert Zwart

  • Affiliations:

  • CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands and Department of Mathematics & Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands and B ...;CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands and Department of Mathematics & Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands and Department of Mathematics & Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

  • Venue:
  • Performance Evaluation - Long range dependence and heavy tail distributions
  • Year:
  • 2005

Quantified Score

Hi-index 0.00

Visualization

Abstract

We derive the sojourn time asymptotics for a multi-class GI/GI/1 queue with regularly varying service requirements operating under the discriminatory processor-sharing (DPS) discipline. DPS provides a natural approach for modelling the flow-level performance of differentiated bandwidth-sharing mechanisms. Under certain assumptions, we prove that the service requirement and sojourn time of a given class have similar tail behaviour, independent of the specific values of the DPS weights. As a by-product, we obtain an extension of the tail equivalence for ordinary processor-sharing (PS) queues to non-Poisson arrivals. The results suggest that DPS offers a potential instrument for effectuating preferential treatment to high-priority classes, without inflicting excessive delays on low-priority classes. To obtain the asymptotics, we develop a novel method which only involves information of the workload process and does not require any knowledge of the steady-state queue length distribution. In particular, the proof method brings sufficient strength to extend the results to scenarios with a time-varying service capacity.