  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.
