A Measure of Dynamical Efficiency for Multimodal Interconnected Urban Systems

Complex network theory describes network performance mostly based on topological characteristics, like betweenness centrality. This work integrates concepts from complex networks and traffic engineering. We propose a new measure for spatial networks and, in particular, for multimodal transportation systems. We give the definition of dynamical efficiency for single- and multi-layer networks. This measure is based on the concept of " reachability " of a location in the city according to the road traffic and to the available modal choice. The dynamical efficiency captures the topological changes in a multilayer network due to the congestion like the average loss in travel time from and to each link and the centrality of intermodal stations. Moreover, we show a method to calculate for each interchange station the so-called dilemma factor, that is a measure of substitutability of the best path choice with an alternative way in an integrated complex variegate transportation system. There are several advantages in using this measure for analyzing a multimodal urban mobility both on the side of the complex network theory and on the practical engineering applications and we briefly illustrated some of them in the conclusion. A detailed application on a megacity has been carried out on a real network with probe traffic data.