An M/G/1 Queuing System with Multiple Vacations to Assess the Performance of a Simplified Deficit Round Robin Model

  • L. Lenzini
  • B. Meini
  • E. Mingozzi
  • G. Stea
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2794)

Abstract

Deficit Round-Robin (DRR) is a packet scheduling algorithm devised for providing fair queuing in the presence of variable length packets. Upper bounds on the buffer occupancy and scheduling delay of a leaky bucket regulated flow have been proved to hold under DRR. However, performance bounds are important for real-time traffic such as video or voice, whereas regarding data traffic average performance indices are meaningful in most of the cases. In this paper we propose and solve a specific worst-case model that enables us to calculate quantiles of the queue length distribution at any time (and hence average delays) as a function of the offered load, when the arrival process is Poissonian. The model proposed is a discrete time discrete state Markov chain of M/G/1-Type, and hence we used the matrix analytic methodology to solve it. The structure of the blocks belonging to the transition probability matrix is fully exploited. As a result of the above exploitation an effective algorithm for computing the matrix G is proposed. The algorithm consists in diagonalizing suitable matrix functions by means of Discrete Fourier Transform and in applying Newton’s method.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • L. Lenzini
    • 1
  • B. Meini
    • 2
  • E. Mingozzi
    • 1
  • G. Stea
    • 1
  1. 1.Department of Information EngineeringUniversity of PisaPisaItaly
  2. 2.Department of MathematicsUniversity of PisaPisaItaly

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