Physics of transportation: Towards optimal capacity using the multilayer network framework

Because of the critical role of transportation in modern times, one of the most successful application areas of statistical physics of complex networks is the study of traffic dynamics. However, the vast majority of works treat transportation networks as an isolated system, which is inconsistent with the fact that many complex networks are interrelated in a nontrivial way. To mimic a realistic scenario, we use the framework of multilayer networks to construct a two-layered traffic model, whereby the upper layer provides higher transport speed than the lower layer. Moreover, passengers are guided to travel along the path of minimal travelling time and with the additional cost they can transfer from one layer to another to avoid congestion and/or reach the final destination faster. By means of numerical simulations, we show that a degree distribution-based strategy, although facilitating the cooperation between both layers, can be further improved by enhancing the critical generating rate of passengers using a particle swarm optimisation (PSO) algorithm. If initialised with the prior knowledge from the degree distribution-based strategy, the PSO algorithm converges considerably faster. Our work exemplifies how statistical physics of complex networks can positively affect daily life.