Eur. Phys. J. B (2013) 86: 146
https://doi.org/10.1140/epjb/e2013-30409-9

Regular Article

Effects of target routing model on the occurrence of extreme events in complex networks

¹ School of Engineering Science, University of Science and Technology of China, Hefei 230026, P.R. China
² School of Transportation Engineering, Hefei University of Technology, Hefei 230009, P.R. China

^a e-mail: humaobin@ustc.edu.cn

Received: 22 May 2012
Received in final form: 16 November 2012
Published online: 10 April 2013

Abstract

This paper investigates the effect of routing protocol on the occurrence of extreme events (EE) in complex networks, as an extension of [V. Kishore, M.S. Santhanam, R.E. Amritkar, Phys. Rev. Lett. 106, 188701 (2011)]. The target routing model [W.X. Wang, B.H. Wang, C.Y. Yin, Y.B. Xie, T. Zhou, Phys. Rev. E 73, 026111 (2006)] is considered. In the model, a tunable power parameter α controls the packets’ preference of forwarding direction. We derive exact expressions for the stationary distribution probability of packets and estimate the occurrence probability of EE on the nodes. The occurrence of EE strongly depends on the routing parameter. For Barabási-Albert scale-free network, Erdös-Rényi random network and Newman-Watts small-world network, it is shown that the minimal occurrence of EE is achieved at α =  −1.