On routing strategy with finite-capacity effect on scale-free networks

We propose a class of systems with finite-capacity effect to investigate routing-strategy optimization. The local topology and the variable capacity, two crucial elements for routing, are naturally coupled by considering the interactions among packets. We show how the combination of these two elements controls the normal and efficient functioning of routing in the frame of condensation and coverage, respectively. Specifically, it is shown that the dynamic behaviors of diffusing packets exhibit condensation, for which exact results of the stationary state and phase transition are given. Further, we explore the diffusion coverage of routed packets through simulation. Various alternatives for the strategy parameters are illustrated to apply standard techniques to alleviate condensation and accelerate coverage. Our results provide a practical way for the design of optimal routing strategies in complex networks by the manipulation of a few parameters.

[1]  Zhiming Zheng,et al.  A new kind of node centrality in directed weighted networks based on the demands of network clients , 2011 .

[2]  Edith Cohen,et al.  Search and replication in unstructured peer-to-peer networks , 2002 .

[3]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[4]  M. Evans,et al.  Nonequilibrium statistical mechanics of the zero-range process and related models , 2005, cond-mat/0501338.

[5]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[6]  Tohru Ikeguchi,et al.  A packet routing method for complex networks by a stochastic neural network , 2007 .

[7]  Condensation in the Zero Range Process: Stationary and Dynamical Properties , 2003, cond-mat/0302079.

[8]  Paul E Parris,et al.  Traversal times for random walks on small-world networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Ricard V. Solé,et al.  Phase Transitions in a Model of Internet Traffic , 2000 .

[10]  Ying-Cheng Lai,et al.  Attack vulnerability of scale-free networks due to cascading breakdown. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Heiko Rieger,et al.  Random walks on complex networks. , 2004, Physical review letters.

[12]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[13]  A. Fronczak,et al.  Biased random walks in complex networks: the role of local navigation rules. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  R K P Zia,et al.  Nature of the condensate in mass transport models. , 2005, Physical review letters.

[15]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[16]  Tao Zhou,et al.  Traffic dynamics based on local routing protocol on a scale-free network. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Jae Dong Noh,et al.  Complete condensation in a zero range process on scale-free networks. , 2005, Physical review letters.

[18]  Zonghua Liu,et al.  Condensation in a zero range process on weighted scale-free networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Alexandre Arenas,et al.  Optimal network topologies for local search with congestion , 2002, Physical review letters.

[20]  M. R. Evans.  Phase transitions in one-dimensional nonequilibrium systems , 2000 .

[21]  Renato Germano,et al.  Traffic of particles in complex networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Jae Dong Noh,et al.  Instability in a network coevolving with a particle system. , 2008, Physical review letters.

[23]  Middleton,et al.  Self-organization and a dynamical transition in traffic-flow models. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[24]  Lada A. Adamic,et al.  Search in Power-Law Networks , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.