Discrete Dynamics in Nature and Society
Volume 2004 (2004), Issue 1, Pages 19-34
doi: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 I. Antoniou et al. 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.