Travel Time Distribution For Network Flows Under Local Routing

When transporting data packets on communication networks, the local routing protocols are often preferred because of the large-scale and complicated property of many realistic network structures such as Internet. Based on a local routing protocol with a navigation parameter proposed in a previous paper [W. X. Wang et al., Phys. Rev. E73, 026111 (2006)], this paper numerically investigates the distribution of travel time for transporting data packets from the origin to the destination in complex networks, including random networks, small-world networks and scale-free networks. Numerical results show that exponential distributions of travel time with various values of exponent in complex networks are obtained. Furthermore, the different values of the exponent can also intuitively prove the previous result for the optimal local routing strategy. Finally, violations of the First-Departure-First-Arrival situation in complex networks are discussed.

[1]  Tao Zhou,et al.  Efficient routing on scale-free networks based on local information , 2006 .

[2]  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.

[3]  Wenjiang Pei,et al.  Mixing search on complex networks , 2010 .

[4]  Shichao Yang.  Exploring complex networks by walking on them. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Wen-Xu Wang,et al.  Integrating local static and dynamic information for routing traffic. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Bo Hu,et al.  Efficient routing on complex networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[9]  Xiang Ling,et al.  Dynamical hysteresis phenomena in complex network traffic. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[12]  G. J. Rodgers,et al.  Traffic on complex networks: Towards understanding global statistical properties from microscopic density fluctuations. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Xiang Ling,et al.  Global dynamic routing for scale-free networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[15]  Nong Ye,et al.  Onset of traffic congestion in complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Tao Zhou,et al.  Mixing navigation on networks , 2007, 0705.0436.

[17]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[18]  Sheng Li,et al.  Integrating fluctuations into distribution of resources in transportation networks , 2009, 0906.0844.

[19]  Rui Jiang,et al.  The effect of bandwidth in scale-free network traffic , 2007 .

[20]  Mao-Bin Hu,et al.  Routing on a weighted scale-free network , 2008 .