Basic characteristics of networks with self-similar traffic simulation

This paper is devoted to simulations the networks with self-similar traffic. The self-similarity in the stochastic process is identified by calculation of the Herst parameter value. Based on the results, received from the experimental research of network perfomance, we may conclude that the observed traffic in real-time mode is selfsimilar by its nature. Given results may be used for the further investigation of network traffic and work on the existing models of network traffic (particularly for new networks concepts like IoT, WSN, BYOD etc) from viewpoint of its cybersecurity. Furthermore, the adequacy of the description of real is achieved by complexifying the models, combining several models and integration of new parameters. Accordingly, for more complex models, there are higher computing abilities needed or longer time for the generation of traffic realization.


Admission
The software tool Wireshark (earlier Ethereal) will be used in order to perform an experimental research of network performance.This is a tool for Ethernet packets analyzing and other networks (sniffer) with open source.The tool has a user graphic interface.The functionality, that is available with Wireshark, is very similar to the abilities of tcpdump tool, however the Wireshark has a praphic user interface and much more possibilities of sorting and filtering of information.The tool allows user to review all the traffic that flows in the network in the real-time mode, transferring it to a network map in promiscuous mode We consider the case of wireless network connection.For the experimental research, we use the network, the scheme of which is illustrated below:

Fig. 5 The results of packets filtering by length
The general information about the interseption session, meaning its beginning, end, amount of packets, average transmission speed is displayed in Comments Summary.

Fig. 6. The general information about interception session
Now we consider one more case of traffic interseption in wireless network connection.The results of packets interseption in the wireless network connection are displayed as follows:   The general information about the interseption session, meaning its beginning, end, amount of packets, average transmission speed is displayed in Comments Summary.The general information about the interseption session, meaning its beginning, end, amount of packets, average transmission speed is displayed in Comments Summary.

Fig. 20. General information about the interseption seanse
We now compare the quantity of intercepted packets for considered cases and performing the graphical illustration.

Conclusions
Traditionally, the self-similarity in the stochastic process is identified by calculation of the Herst (H) parameter value.The fact, that , meaning that Herst parameter is different of 0.5, is an enough reason to state that the process is self-similar.Not to mention, that the value of a Herst parameter which is close to one, may mean that the process is determined, not random: for a gange of strictly-determined processes, structure is strictly repeated on any scale, which leads to "one" value of Herst parameter.Based on the results, that were received from the experimental research of network perfomance, dispersion -time interdependence for the intercepted traffic and the slope of line , we may conclude that the observed traffic in real-time mode is self-similar by its nature.The results of this paper may be used for the further investigation of network traffic and work on the existing models of network traffic.Furthermore, the adequacy of the description of real is achieved by complexifying the models, combining several models and integration of new parameters.Accordingly, for more complex models, there are higher computing abilities needed or longer time for the generation of traffic realization.

Fig. 1 .
Fig. 1.The scheme of an experimental research networkThe results of packets interception in the wireless network connection are displayed as:

Fig. 2 .Fig. 3 .
Fig. 2. Intercepted packetsIt is possible to receive the graphical illustration of intercepted traffic for certain timeframe with the help of tool features, for instance:

Fig. 4 .
Fig. 4. Hierarchy of protocols With the help of a packet length filter (Lauching Wireshark  Wireless network connection  Start  Statistics  Packet Lengths) we receive the quantity of packets of various duration, their percentage, range of minimum and maximum values of packets etc.

Fig. 7 .Fig. 8 .
Fig. 7. Intercepted packetsWith the help of tool features, it is possible to get the graphical illustration of intersepted traffic for certain timeframe, for instance:

Fig. 9 .
Fig. 9. Protocol hierarchy With the help of a packet length filter we receive the quantity of packets of various duration, their percentage, range of minimum and maximum values of packets, etc.

Fig. 10 .
Fig. 10.The results of packets filtering by length

Fig. 11 .
Fig. 11.The general information about interception session In addition, it is possible to get the quantity of HTTP and IP protocol types, if necessary.It should be done as follows: Lauching Wireshark -> Wireless network connection -> Start -> Statistics -> HTTP -> Packet Counter or Lauching Wireshark -> WWireless network nonnection -> Start -> Statistics -> IP Statistics -> IP Protocol Types accordingly.

Fig. 15 .
Fig. 15.Graphic illustration of intersepted trafficWith the help of a packet length filter, we receive the quantity of packets of various duration, their percentage, range of minimum and maximum values of packets, etc.

Fig. 16 .
Fig. 16.The results of packets filtering by lengthThere is a possibility of percentage analysis of different protocols after the data alanysis.To access the protocols hierarchy statistics following steps are needed: Launching Wireshark -> Local network connection -> Start -> Statistics -> Protocol Hierarchy.

Fig. 17 .
Fig. 17.Protocol hierarchy In addition, it is possible to get the quantity of HTTP and IP protocol types, if necessary.It should be done as follows: Lauching Wireshark -> Wireless network connection -> Start -> Statistics -> HTTP -> Packet Counter or Lauching Wireshark -> WWireless network nonnection -> Start -> Statistics -> IP Statistics -> IP Protocol Types accordingly.

Fig. 21 .
Fig. 21.Compairing the results of filtering packets by lengthWe now check if the experimentally received flow is self-similar.The Dispersion -time interdependence for the intercepted traffic:

Fig. 22 .
Fig. 22. Dispersion -time interdependence for the intercepted traffic The reseived slope of line equals .With the help of it we can calculate the self-similarity coefficient .The resulting scope of line equals 0,1687.It means that the value of Herst parameter is 0,8313, which is equal to value of Herst parameter for the self-similar traffic ( ).