  Multilayer networks describe well many real interconnected communication and
transportation systems, ranging from computer networks to multimodal mobility
infrastructures. Here, we introduce a model in which the nodes have a limited
capacity of storing and processing the agents moving over a multilayer network,
and their congestions trigger temporary faults which, in turn, dynamically
affect the routing of agents seeking for uncongested paths. The study of the
network performance under different layer velocities and node maximum
capacities, reveals the existence of delicate trade-offs between the number of
served agents and their time to travel to destination. We provide analytical
estimates of the optimal buffer size at which the travel time is minimum and of
its dependence on the velocity and number of links at the different layers.
Phenomena reminiscent of the Slower Is Faster (SIF) effect and of the Braess'
paradox are observed in our dynamical multilayer set-up.
