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On a kinetic model of the internet traffic. (English) Zbl 1098.90013
Summary: 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.
90B18 Communication networks in operations research
82C99 Time-dependent statistical mechanics (dynamic and nonequilibrium)
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