Scaling in transportation networks

Subway systems span most large cities, and railway networks most countries in the world. These networks are fundamental in the development of countries and their cities, and it is therefore crucial to understand their formation and evolution. However, if the topological properties of these networks are fairly well understood, how they relate to population and socio-economical properties remains an open question. We propose here a general coarse-grained approach, based on a cost-benefit analysis that accounts for the scaling properties of the main quantities characterizing these systems (the number of stations, the total length, and the ridership) with the substrate's population, area and wealth. More precisely, we show that the length, number of stations and ridership of subways and rail networks can be estimated knowing the area, population and wealth of the underlying region. These predictions are in good agreement with data gathered for about $140$ subway systems and more than $50$ railway networks in the world. We also show that train networks and subway systems can be described within the same framework, but with a fundamental difference: while the interstation distance seems to be constant and determined by the typical walking distance for subways, the interstation distance for railways scales with the number of stations.Comment: 8 pages, 6 figures, 1 table. To appear in PLoS On

The simplicity of planar networks

Shortest paths are not always simple. In planar networks, they can be very different from those with the smallest number of turns - the simplest paths. The statistical comparison of the lengths of the shortest and simplest paths provides a non trivial and non local information about the spatial organization of these graphs. We define the simplicity index as the average ratio of these lengths and the simplicity profile characterizes the simplicity at different scales. We measure these metrics on artificial (roads, highways, railways) and natural networks (leaves, slime mould, insect wings) and show that there are fundamental differences in the organization of urban and biological systems, related to their function, navigation or distribution: straight lines are organized hierarchically in biological cases, and have random lengths and locations in urban systems. In the case of time evolving networks, the simplicity is able to reveal important structural changes during their evolution.Comment: 8 pages, 4 figure

Elementary processes governing the evolution of road networks

Urbanisation is a fundamental phenomenon whose quantitative characterisation is still inadequate. We report here the empirical analysis of a unique data set regarding almost 200 years of evolution of the road network in a large area located north of Milan (Italy). We find that urbanisation is characterised by the homogenisation of cell shapes, and by the stability throughout time of high-centrality roads which constitute the backbone of the urban structure, confirming the importance of historical paths. We show quantitatively that the growth of the network is governed by two elementary processes: (i) `densification', corresponding to an increase in the local density of roads around existing urban centres and (ii) `exploration', whereby new roads trigger the spatial evolution of the urbanisation front. The empirical identification of such simple elementary mechanisms suggests the existence of general, simple properties of urbanisation and opens new directions for its modelling and quantitative description.Comment: 10 pages, 6 figure

Evoluzione della rete italiana delle autostrade del mare

Le Autostrade del Mare sono dei servizi di trasporto marittimo a corto raggio (Short Sea Shipping) che hanno fondamentalmente i seguenti obiettivi: costituire una valida alternativa al trasporto di tipo “tuttostrada”; ed integrare i trasporti terrestri, in particolare quando esistono dei vincoli geografici. In questa nota, dopo alcune osservazioni sulla competitività dei servizi di trasporto intermodale basati sulle Autostrade del Mare, rispetto ai servizi di trasporto “tutto-strada”, si analizza lo sviluppo delle rotte da e per i porti italiani. Lo studio mette in evidenza che le rotte delle Autostrade del Mare, fra coppie di porti italiani sulla penisola, non rappresentano, almeno attualmente, un’alternativa efficace al trasporto “tutto-strada”; anche se vi sono dei segni di una inversione di tendenza. Le rotte nazionali delle Autostrade del Mare infatti integrano i collegamenti fra la penisola e le isole; le rotte internazionali delle Autostrade del Mare collegano, fondamentalmente, i porti adriatici con porti della penisola balcanica, in particolare quelli posti sull’altra sponda dell’Adriatico, e i porti tirrenici con i porti, europei e nord africani, del Mediterraneo Occidentale. La nota mette infine in evidenza l’evoluzione delle caratteristiche dei servizi delle Autostrade del Mare negli anni 2008, 2010 e 2012. Seguono alcune considerazioni: sulla competitività del traspoto intermodale, basato su Autostrade del Mare, rispetto al tutto-strada ed sulle azioni relative ad azioni di policy volte a migliorare questa competitività