Transport network analysis

For transportation network mathematical graph theory, see Flow network.

A transport network, or transportation network is a network or graph in geographic space, describing an infrastructure that permits and constrains movement or flow. Examples include but are not limited to road networks, railways, air routes, pipelines, aqueducts, and power lines. The digital representation of these networks, and the methods for their analysis, is a core part of spatial analysis, geographic information systems, public utilities, and transport engineering. Network analysis is an application of the theories and algorithms of Graph theory and is a form of proximity analysis.

Network Data

Network analysis requires detailed data representing the elements of the network and its properties. The core of a network dataset is a vector layer of polylines representing the paths of travel, either precise geographic routes or schematic diagrams, known as edges. In addition, information is needed on the network topology, representing the connections between the lines, thus enabling the transport from one line to another to be modeled. Typically, these connection points, or nodes, are included as an additional dataset.

Both the edges and notes are attributed with properties related to the movement or flow:

• Capacity, measurements of any limitation on the volume of flow allowed, such as the number of lanes in a road, telecommunications bandwidth, or pipe diameter.
• Impedance, measurements of any resistance to flow or to the speed of flow, such as a speed limit or a forbidden turn direction at a street intersection
• Cost accumulated through individual travel along the edge or through the node, commonly elapsed time, in keeping with the principle of friction of distance. For example, a node in a street network may require a different amount of time to make a particular left turn or right turn. Such costs can vary over time, such as the pattern of travel time along an urban street depending on diurnal cycles of traffic volume.
• Flow volume, measurements of the actual movement taking place. This may be specific time-encoded measurements collected using sensor networks such as traffic counters, or general trends over a period of time, such as Annual average daily traffic (AADT).

Analysis Methods

Transport network analysis is used to determine the flow of vehicles (or people) through a transport network, typically using mathematical graph theory. It may combine different modes of transport, for example, walking and car, to model multi-modal journeys. Transport network analysis falls within the field of transport engineering. Traffic has been studied extensively using statistical physics methods. Recently a real transport network of Beijing was studied using a network approach and percolation theory. The research showed that one can characterize the quality of global traffic in a city at each time in the day using percolation threshold, see Fig. 1. In recent articles, percolation theory has been applied to study traffic congestion in a city. The quality of the global traffic in a city at a given time is by a single parameter, the percolation critical threshold. The critical threshold represents the velocity below which one can travel in a large fraction of city network. The method is able to identify repetitive traffic bottlenecks. Critical exponents characterizing the cluster size distribution of good traffic are similar to those of percolation theory. It is also found that during rush hours the traffic network can have several metastable states of different network sizes and the alternate between these states.

An empirical study regarding the size distribution of traffic jams has been performed recently by Zhang et al. They found an approximate universal power law for the jam sizes distribution.

A method to identify functional clusters of spatial-temporal streets that represent fluent traffic flow in a city has been developed by Serok et al. G. Li et al. developed a method to design an optimal two layer transportation network in a city.

Fig. 1: Percolation of traffic networks in a typical day in Beijing. A Shows the high speed clusters. In B one can see the clusters at the critical threshold, where the giant component breaks. C Shows the low speed case where one can reach the whole city. In D, one can see the percolation behavior of the largest (green) and second largest (orange) components as a function of relative speed. E Shows the critical threshold, q$c$, during the day for working days and weekends. High q$c$ means good global traffic while low q$c$ is bad traffic—during rush hour.

Flow patterns of traffic

River-like patterns of traffic flow in urban areas in large cities during rush hours and non rush hours have been studied by Yohei Shida et al.

See also

• Braess's paradox
• Flow network
• Heuristic routing
• Interplanetary Transport Network
• Network science
• Percolation theory
• Street network
• Rail network
• Multimodal transport