Stochastic Model of Internet Access Patterns: Coexistence of Stationarity and Zipf-Type Distributions

Masaki AIDA  Tetsuya ABE  

IEICE TRANSACTIONS on Communications   Vol.E85-B   No.8   pp.1469-1478
Publication Date: 2002/08/01
Online ISSN: 
Print ISSN: 0916-8516
Type of Manuscript: PAPER
Category: Fundamental Theories
Internet,  destination address,  LRU stack,  Zipf's law,  caching,  

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This paper investigates the stochastic property of packet destinations in order to describe Internet access patterns. If we assume a sort of stationary condition for the address generation process, the process is an LRU stack model. Although the LRU stack model gives appropriate descriptions of address generation on a medium/long time-scale, address sequences generated from the LRU stack model do not reproduce Zipf-type distributions, which appear frequently in Internet access patterns. This implies that the address generation behavior on a short time-scale has a strong influence on the shape of the distributions that describe frequency of address appearances. This paper proposes an address generation algorithm that does not meet the stationary condition on the short time-scale, but restores it on the medium/long time-scale, and shows that the proposed algorithm reproduces Zipf-type distributions.