A new goodness of fit test for histograms regarding network traffic packet size process

Contemporary communication is becoming more and more complex and extensive. Network planners very often use simulations tools for reducing the costs of planning, constructions, and maintenances. Modeling network traffic is also a very important challenge regarding simulation tools, especially the modeling of measured traffic as to which would be the best approximation of measured traffic in real network. This is possible to ensure using the accurate descriptions of two random processes, both of which define network traffic. These two random processes are packet size process and inter-arrival time. In stochastic modeling both of these processes are modeled using probability distributions. The parameters of these distributions are estimated in an empirical manner with the help of histograms regarding measured traffic processes. Any accuracy regarding suitable distribution between distribution and histogram can be evaluated using different tests, such as Kolmogorov-Smirnov or Chi-square. However, during the measurements and modeling of measured network traffic these tests show one weakness in the case of trying to model network traffic, in regard to the best approximation of measured traffic in bit and packet-rates at the same time. So we have developed a new and better goodness of fit test of network traffic, which considers the number of packets and also the packet’s size. Using simulations we show, that the use of this new more suitable test leads to better choice regarding distribution when describing a packet size process, which than consequently, also lead to smaller discrepancies between measured and simulated traffic in bit and packet-rates.