Some Methods of Probability Theory in NanoNET Wireless Networks Analysis

Heavy-tailed distributions nowadays play an important role in network analysis. More and more papers discussing their presence in one or another network environment are submitted. Presence of heavy-tails and long range dependence in physical, biological, social processes and their evidence in contemporary computing systems has for several years focused the attention of scientists in applied mathematics, especially, probability theory.

Recent researches have highlighted the presence of heavy tails in wireless environment. Some random variables related to characteristics of wireless networks were shown to have heavy-tailed distribution (c.f. A QoS Framework for Heavy-tailed Traffic over the Wireless Internet. Zhenwen Shao, Upamanyu Madhow). Moreover, some works are dedicated to developing new approaches in existent protocols to achieve best Quality of Service and to minimize the effect of heavy-tails on system performance. (c.f. Scheduling Heavy-tailed Data Traffic over the Wireless Internet. Zhenwen Shao, Upamanyu Madhow.)

Our work is dedicated to using heavy-tailed approach and some methods of analysis of heavy-tailed distributions in wireless networks based on the contemporary and dynamically developing NanoNET technology. For instance, a chaotic map is built based on the measurements taken from NanoNET environment. (This work in IEEE 802.11 networks is discussed in the following article: Chaotic Maps as Parsimonious Bit Error Models of Wireless Channels. Andreas K\"orke, Andreas Willig, Holger Karl.) Chaotic maps achieve modeling accuracy and is one of the best models for heavy-tailed processes, despite having only six parameters. It's parameters have clear intuitive meaning and are easy to direct manipulation.