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Discrete Dynamics in Nature and Society
Volume 2004 (2004), Issue 1, Pages 19-34
http://dx.doi.org/10.1155/S1026022604312033

On a kinetic model of the internet traffic

1Department of Mathematics, Aristotele University of Thessaloniki, Campus Box 121, Thessaloniki 54124, Greece
2Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna 141980, Russia
3Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna 141980, Russia

Received 11 December 2003

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present the modification of the Prigogine-Herman kinetic equation related to the network traffic. We discuss a solution of this equation for homogeneous time-independent situations and for the lognormal desired speed distribution function, obtained from the traffic measurements. This solution clearly shows two modes corresponding to individual flow patterns (low concentration mode) and to collective flow patterns (traffic jam mode). For situations with low concentration, there is almost a linear dependence of the information flow versus the concentration and the higher the average speed the lower the concentration at which the optimum flow takes place. When approaching the critical concentration, there are no essential differences in the flow for different average speeds, whereas for the individual flow regions there are dramatic differences.