Jamming in weighted scale-free gradient networksB. Wang1, 2, K. Aihara1, 2 and L. Chen3
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
received 17 March 2008; accepted in final form 4 June 2008; published July 2008
published online 3 July 2008
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 can be adjusted to be or . With the new definition of the jamming coefficient, we numerically calculate the jamming coefficient as a function of , the connectivity , and the degree exponent . The results indicate that for each , 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.
89.75.-k - Complex systems.
89.75.Hc - Networks and genealogical trees.
87.23.Ge - Dynamics of social systems.
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