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We numerically investigate the influence of the structural properties of small-world network on the traffic delivery, by incorporating local traffic information into the shortest path routing policy. We focus on the network capacity that can be measured by the critical value of phase transition from free flow to congestion. Here we address influence of the topology on the dynamics of traffic delivery for small-world networks, taking into account the average degree, the average clustering coefficient, and the information-processing capacity of individual nodes. Simulation results show that the critical value is obviously different for different small world network structures, and the critical value increases as the average degree increases. Moreover, compared to the influence of the average degree on traffic delivery, the influence of the average clustering coefficient on traffic delivery is less important role.