## Discrete map for traffic simulation

**Belkov D.V., Edemskaya E.N. **

One of the most important mathematical discoveries of the past few decades is that random behavior can arise in deterministic nonlinear systems with just a few degrees of freedom. This discovery gives new hope to providing simple mathematical models for analyzing systems. The analysis of the network traffic is actually reduced to the task of processing the time series. The theory of non-linear dynamics provides a potential to study, identification and prediction of the time series that have some specific properties. Recent studies of real traffic data in modern computer networks have shown that traffic exhibits self-similar (fractal) properties. The use of traditional models in networks characterized by self-similar processes can lead to incorrect conclusions about the performance of analyzed networks. Many analytical studies have shown that self-similar network traffic can have a detrimental impact on network performance, including amplified queuing delays and packet loss rates in broadband wide area networks The understanding of the self-similar nature in traffic is an important issue. One of the most important tasks of network research is to construct adequate models for the concerned traffic flows. The objective of our work is deterministic traffic simulation. The task of this work is design of one dimension discrete map for traffic simulation. Discrete maps can produce broad traffic models in the sense that sometimes even one parameter is enough to produce the range of behavior that appears in packet traffic. The discrete map for network traffic simulation is offered in this work. In this article the researches are executed in the Matlab environment. For the study two realization of network traffic is chosen. They are got in the university of city Napoly (Italy). In obedience to a license information is freely accessible for the analysis. Studied time series are the measuring of TCP-packet jitter. In first case (TCP_j512) packets have a volume a 512 byte, in the second (TCP_j1024) is a 1024 byte. The measuring were conducted every 10 milliseconds, over 2000 counting out is got. A sender had 802.11b connection, a recipient is UMTS-access, speed of transmission 100 pps. In the article for the simulation of these time series it is suggested to use the discrete map, that built on the basis of the map “tent” and Zaborovsky map. The simulation of TCP-packets jitter of wireless network is executed. Phase trajectories of models and real processes have same type. The offered discrete displaying can be used for bursty traffic simulation.