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Statistical Properties of the Congestion Process of Particle Delivering on scale-free network

In this paper, we propose a particle delivering model on scale-free network with shortest-path algorithm and preferential-walk algorithm, by the latter of which the congested vertex is steered clear of. By analyzing the number of over-capacity vertices and the cumulative particle lifetime, we study the statistical properties of the congestion process of such a particle delivering model. The results show that the number of over-capacity vertices forms punctuated equilibrium processes, which indicate the difficulties of studying network congestion from the macroscopical point of view by analyzing the number of particles on the network. And the average number of over-capacity vertices under each local punctuated equilibrium process has a power-law relationship with the local punctuated equilibrium value. The analysis of the cumulative particle lifetime indicates the different roles of shortest-path and preferential-walk in particle delivering on complex networks.