Volume 123, Number 5, September 2018
|Number of page(s)||7|
|Published online||02 October 2018|
Universal rank-size statistics in network traffic: Modeling collective access patterns by Zipf's law with long-term correlations
1 Radio Systems Department, St. Petersburg Electrotechnical University - 5 Professor Popov street, St. Petersburg, 197376 Russia
2 Department of Information Technologies, Ivanovo State University - 39 Ermak street, Ivanovo 153025 Russia
Received: 4 April 2018
Accepted: 3 September 2018
We analyze network traffic rank-size statistics at different levels and organization. Our results support the emergence of Zipf's law in the rank-size traffic distributions by time, source and destination. The corresponding empirical laws considering typical discreteness and finite-size effects can be well approximated by q-exponential distributions for external IPs as well as by β- and Γ-distributions for internal LAN IPs and time fragments, respectively. Once appropriately normalized, the observed rank-size statistics exhibit rather universal shapes that are well reproduced by nonextensive entropy maximization algorithm for finite system sizes and can be used to model typical network activity patterns for a given community with a given number of active nodes as a sole free parameter.
PACS: 02.50.-r – Probability theory, stochastic processes, and statistics / 05.10.-a – Computational methods in statistical physics and nonlinear dynamics / 89.20.Hh – World Wide Web, Internet
© EPLA, 2018
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