An M/G/1 Queuing System with Multiple Vacations to Assess the Performance of a Simplified Deficit Round Robin Model
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.
KeywordsPacket Arrival Packet Length Markovian Arrival Process Buffer Occupancy Queue Length Distribution
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