An Information Theoretic Approximation for Modelling Computer Network Nodal Queuing Delay: A Congestion Measure

Abstract

A method for modelling the congestion measure of computer node delay due to the queuing representative of general (GI/G/1) and specific queuing systems is developed. The basic technique is the formulation of a computer node queuing mean waiting time from a discrete marginal customer per time slot solution of a continuous marginal time per customer pdf. The information theory idea of quantization is utilized to numerically determine the areas of sections (quantiles) of the pdf of the marginal customers per time slot. These quantiles represent the entries of the probability transition matrix of the change of the number of customers in the queue for the irreducible Markov Chains of uniform quantization upper and lower bound steady state solutions for the number of customers in the queue at time slot j. The marginal pdf area considered is normalized to one resulting in the computation of normalized quantile areas for the probability transition matrix required for the steady state upper and lower bound buffer occupancy solutions. The mean waiting time is then the summation of the L+1(L=length of the computer node queue) steady state buffer occupancy solutions multiplied by the corresponding number of customers in the computer node queue.