On the critical packet injection rate of a preferential next-nearest neighbor routing traffic model on Barabási-Albert networks

DOI10.1140/EPJB/E2009-00411-1zbMATH Open1189.91177arXiv0906.0846OpenAlexW3103748852MaRDI QIDQ978940

Publication date: 25 June 2010

Published in: The European Physical Journal B. Condensed Matter and Complex Systems (Search for Journal in Brave)

Abstract: Recently, Yin et al. [Eur. Phys. J. B 49, 205 (2006)] introduced an efficient small-world network traffic model using preferential next-nearest neighbor routing strategy with the so-called path iteration avoidance (PIA) rule to study the jamming transition of internet. Here we study their model without PIA rule by a mean-field analysis which carefully divides the message packets into two types. Then, we argue that our mean-field analysis is also applicable in the presence of PIA rule in the limit of a large number of nodes in the network. Our analysis gives an explicit expression of the critical packet injection rate

R_{c}

as a function of a bias parameter of the routing strategy

a l p h a

in their model with or without PIA rule. In particular, we predict a sudden change in

R_{c}

at a certain value of

a l p h a

. These predictions agree quite well with our extensive computer simulations.

Full work available at URL: https://arxiv.org/abs/0906.0846

Mathematics Subject Classification ID

Social networks; opinion dynamics (91D30) Small world graphs, complex networks (graph-theoretic aspects) (05C82)

Cites Work

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