Jamming in weighted scale-free gradient networks

¹  ERATO Aihara Complexity Modelling Project, JST, Institute of Industrial Science, The University of Tokyo 4-6-1 Komaba, Meguro-ku, Tokyo, 153-8505, Japan
²  Institute of Industrial Science, The University of Tokyo - Tokyo, Japan
³  Department of Electrical Engineering and Electronics, Osaka Sangyo University - Daito, Osaka, 574-8530, Japan

Corresponding authors: bwang@aihara.jst.go.jp aihara@sat.t.u.-tokyo.ac.jp

Received: 17 March 2008
Accepted: 4 June 2008

Abstract

In this paper we investigate the jamming degree in weighted scale-free gradient networks, where the gradient flow is described as the edge weight , which is related with the end-point degrees of a link, and α can be adjusted to be or . With the new definition of the jamming coefficient, we numerically calculate the jamming coefficient as a function of α, the connectivity , and the degree exponent γ. The results indicate that for each γ, there exists an optimal value of , at which the jamming coefficient is minimized. The value of depends on the connectivity . With the increase of , shifts from zero to the minimum value we examined. Furthermore, there exists a critical value of , which is numerically estimated to be about 0.5. Namely, when , a homogeneous network will get a higher level of congestion, otherwise, the opposite will happen.