Network traffic research by the Hurst function
Recent studies of real traffic data in modern computer networks have shown that traffic exhibits self-similar (or fractal) properties over a wide range of time scales. The properties of self-similar traffic are very different from the traditional models of traffic based on Poisson, Markov-modulated Poisson, and related processes. The use of traditional models in networks characterized by self-similar processes can lead to incorrect conclusions about the performance of analyzed networks. These include serious over-estimations of the performance of computer networks, insufficient allocation of communication and data processing resources, and difficulties ensuring the quality of service expected by network users. The self-similar network traffic can have a detrimental impact on network performance, including amplified queuing delay, retransmission rate and packet loss rate. Modern network traffic consists of more bursts than Poisson models predict over many time scales. This difference has implications for congestion control mechanisms and performance. Research of network traffic is important, as a fractal traffic in modern computer networks worsens quality of service. Research of the real traffic for the exposure of its characteristic features is the purpose of the work. For research of fractal processes the Hurst index H, which is the measure of duration of long-term dependence of process is used. In the article for the traffic analysis it is suggested to use the Hurst function. Its graph is built as follows. On abscising axis we put aside the values N=2,3,…,Nm, where Nm is maximal length of temporal row, N is current amount of elements of temporal row. For every value N we determine the size of the Hurst H(N) index and put aside it on a y-axis. Researches are executed in the Matlab environment. For the study four realization of network traffic is chosen, got in the university of Napoly city (Italy). In obedience to a license information is freely accessible for the analysis. The studied temporal rows are measuring of the UDP delay and TCP-packets. In first case (time-series UDP_d64) UDP packets have a volume a 64 byte, in the second (time-series UDP_d512) is a 512 byte. Third time-series (TCP_d64) is the transmission of TCP-packets of volume is a 64 byte, fourth time-series (TCP_d512) is the transmission of TCP- packets of volume is a 512 byte. Next results are got. The traffic UDP_d64 consists of two persistent states and phase transition between states in moment when the Hurst function achieves the value H=0,5. The traffic UDP_d512 has phase transition from an antipersistent state (H=0,25) to the state of homogeneous traffic (H=0,5) and gradual return to antipersistent state. The TCP-traffic has gradual return from persistent to homogeneous state, homogeneous mode, phase transition to the persistent state and gradual return from persistent state to homogeneous state.