Dynamical Efficiency in congested road networks

The main topological properties of a transportation network can be characterized using different criteria such as structure, the degree distribution of nodes, connectivity and some clustering aspects. Efficiency is a property of a network that identifies the easiness for a walker in a graph to reach different nodes in the network given its position (see Latora and Marchiori (2007) for more details). Efficiency, in its static form, has been widely utilized in several spatial networks like communication, social and transportation networks and it is quite established in physical sciences. In this study, we aim to compute the efficiency of the network and track its changes over time by considering average link speed in a city during congestion period. To quantify the time efficiency, we introduce a metric that involves time and not space taking into account the average measured (or estimated) speed for the links during the peak hour. The main idea is to compute the shortest travel times using average link speed that represent traffic condition in the network. For any given node in the network (graph), we compute all (or a part of based, for example, in an OD matrix) shortest travel time starting from that node. Hence, we have a quantitative analysis of the time efficiency for each road. Furthermore, we can divide the city into regions with different levels of efficiency and visualize them.