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Nonlinear dynamical models of the network traffic

Keywords:

A. V. Kolesnikov – Post-graduate student of the “Theoretical Informatics and Computer Technologies” department, Bauman Moscow State Technical University
I. P. Ivanov – Ph.D. (Eng.), vice-rector on informatization, head of the “Theoretical Informatics and Computer Technologies” department, Bauman Moscow State Technical University
M. A. Basarab – Dr. Sc. (Phys.-Math.), professor of «Information Security» department, Bauman Moscow State Technical University


In computer processing and storage of information it is necessary to exchange data between the actors. So, since late 70s the rapid development of computer networks and related equipment begins. Local and wide area networks evolve every year. The number of connected subscribers increases, as well as the total amount of transmitted information. This fast development trend raises a number of problems. Intensive exchange of data requires increased computing power and can lead to a reduction in the quality of service (QoS). Network topology, transportation protocol, different types of web services and many other reasons can influence on characteristics of data traffic. So the actual mathematical models of traffic which could help to optimize the network load are needed. They are also will be useful in developing software and hardware tools for increasing network reliability. Obviously, that macro parameters of network traffic are determined by administrators. But the parameters on timescales of microseconds are defined by hardware and transportation environment. So research of servers hardware and operating system behavior could be another useful instrument in the task of network load optimization. Investigation of the memory layout, CPU, operating system state and other characteristics of the host may reveal hidden correlations, cycles and phase transitions in the network traffic distribution. In this work, on the example of a Bauman MSTU corporative network server, methods for nonlinear analysis of incoming and outgoing traffic dynamical characteristics are considered. The Lyapunov exponent and Hurst exponent of the network traffic, characterizing chaotic properties of the processes, were evaluated. Phase diagrams of traffic were investigated and attractors were revealed, allowing detailed analysis of the impact of load on the network traffic capacity. For all processes, the self-similarity was found, confirming the possibility of using fractal models for working with data, including the prediction of the behavior of the time series. A simulation model of a computer network is developed and its main characteristics are investigated. Conclusions about the applicability of the developed model to study the real corporate network are made.
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