Designing an efficient routing strategy is of great importance to alleviate traffic congestion in multilayer networks. In this work, we design an effective routing strategy for multilayer networks by comprehensively considering the roles of nodes local structures in micro-level, as well as the macro-level differences in transmission speeds between different layers. Both numerical and analytical results indicate that our proposed routing strategy can reasonably redistribute the traffic load of the low speed layer to the high speed layer, and thus the traffic capacity of multilayer networks are significantly enhanced compared with the monolayer low speed networks. There is an optimal combination of macro- and micro-level control parameters at which can remarkably alleviate the congestion and thus maximize the traffic capacity for a given multilayer network. Moreover, we find that increasing the size and the average degree of the high speed layer can enhance the traffic capacity of multilayer networks more effectively. We finally verify that real-world network topology does not invalidate the results. The theoretical predictions agree well with the numerical simulations.
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