An M/G/1 queuing system with multiple vacations to assess the performance of a simplified deficit round Robin model

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. © Springer-Verlag Berlin Heidelberg 2003.