Wednesday, 27 February 2013

Urban Road Usage Patterns


In an era of unprecedented global urbanization, society faces a rapidly accelerating demand for mobility, placing immense pressure on urban road networks. This demand manifests in the form of severe traffic congestion, which decreases the roads’ level of service, while at the same time increasing both fuel consumption and traffic-related air pollution.

In this blog post, we look at a methodology, which employs comprehensive mobile phone data to detect patterns of road usage and the origins of the drivers. Thus, providing a basis for better informed transportation planning, including targeted strategies to mitigate congestionWe formalize the problem by counting the observed number of individuals moving from one location to another, which we put forward as the transient origin destination (t-OD) matrix.

To study the distribution of travel demands over a day we divide it into four periods (Morning: 6 am–10 am, Noon & Afternoon: 10 am–4 pm, Evening: 4 pm–8 pm, Night: 8 pm–6 am) and cumulate trips over the total observational period. A trip is defined when the same mobile phone user is observed in two distinct zones within one hour (zones are defined by 892 towers’ service areas in the San Francisco Bay Area and by 750 census tracts in the Boston Area). In the mobile phone data, a user’s location information is lost when he/she does not use his/her phone, but by defining the transient origin and destination with movements within one hour, we can capture the distribution of travel demands. Specifically we calculate the t-OD as:
where A is the number of zones. W is the one-hour total trip production in the studied urban area, a number readily available for most cities. However this number gives no information about the trip distribution between zones, which we can enhance by the information gained via mobile phones. Directly from the mobile phone data we calculate Tij(n), which is the total number of trips that user nmade between zone i and zone j during the three weeks of study. Via calibrating Tij(n) for the total population we obtain:  , where Nk is the number of users in zone k. The ratio M scales the trips generated by mobile phone users in each zone to the trips generated by the total population living there: M(k) = Npop(k)/Nuser(k), where Npop(k) and Nuser(k) are the population and the number of mobile phone users in zone k. Furthermore to assign only the fraction of the trips attributed to vehicles, we correct Fallij by the vehicle usage rate, which is a given constant for each zone and therefore obtain Fvehicleij .
For each mobile phone user that generated the t-OD, we can additionally locate the zone where he or she lives, which we define as the driver source. Connecting t-ODs with driver sources allows us for the first time to take advantage of mobile phone data sets in order to understand urban road usage. In the following, we present the analysis of the road usage characterization in the morning period as a case study.


A road network is defined by the links representing the road segments and the nodes representing the intersections. Using incremental traffic assignment, each trip in the t-OD matrix is assigned to the road network, providing us with estimated traffic flows (Fig.1(a)). The road network in the Bay Area serves a considerable larger number of vehicles per hour (0.73 million) than the one in the Boston (0.54 million). The traffic flow distribution P(V) in each area can be well approximated as the sum of two exponential functions corresponding to two different characteristic volumes of vehicles (Fig. 1a); one is the average traffic flow in their arterial roads (vA) and the other is the average traffic flow in their highways (vH). We measure  (R2>0.99) with vA = 373 (236) vehicles/hour for arterials and vH = 1,493 (689) vehicles/hour for highways in the Bay Area (Boston numbers within parenthesis, pA and pH are the fraction of arterial roads and the fraction of highways). Both road networks have similar number of arterials (~20,000), but the Bay Area with more than double the number of highways than Boston (3,141 highways vs 1,267 in Boston) still receives the double of the average flow in the highways (vH) and a larger average flow in the arterial roads.

Figure 1: Distributions of traffic flow, betweenness centrality and VOC in the two urban areas.

Distributions of traffic flow, betweenness centrality and VOC in the two urban areas.
(a) The one-hour traffic flow V follows a mixed exponential distribution for both Bay Area and Boston Area, where constants pA and pare the fraction of arterial roads and the fraction of highways, vA and vH is the average traffic flow for arterial roads and highways respectively. (b) The distribution of road segment’s betweenness centrality bc is well approximated by  , where the power-law distribution approximates arterial roads’ bc distribution and the exponential distribution approximates highways’ bc distribution. βHdenotes the average bc of highways and αA is the scaling exponent for the power-law. (c) The volume over capacity VOC follows an exponential distribution P(VOC) = γe−VOC/γ with an average VOC = 0.28 for the two areas. Traffic flows in most road segments are well under their designed capacities, whereas a small number of congested segments are detected.
The volume of vehicles served by a road depends on two aspects: the first is the functionality of the road according to its ability to be a connector based on its location in the road network (i.e. betweenness centrality) and the second is the inherent travel demand of the travelers in the city. The betweenness centrality bc of a road segment is proportional to the number of shortest paths between all pairs of nodes passing through it: we measured bc by averaging over each pair of nodes, and following the shortest time to destination. The two road networks, analyzed here, have completely different shapes: the Bay Area is more elongated and connects two sides of a bay, while the Boston Area follows a circular shape (Fig. 2a). But both have a similar function in the distribution of bc: with a broad term corresponding to the arterial roads and an exponential term to the highways, which is at the tail of larger bc. As Fig. 1b shows, we measure: P(bc) =pAPA(bc) + pHPH(bc) (R2>0.99), with  for arterial roads and  for highways. The highways in the Bay Area have an average bc of βH = 2.6 × 10−4, whereas a largerβH = 4.6 × 10−4 is found for the Boston Area highways, indicating their different topological structures. Interestingly, despite, the different topologies of the two road networks, the similar shapes of their distribution of traffic flows indicate an inherent mechanism in how people are selecting their routes. 
Figure 2: Tracing driver sources via the road usage network.
Tracing driver sources via the road usage network.(a) The colour of a road segment represents its degree Kroad. Most residential roads are found to have small Kroad, whereas the backbone highways and the downtown arterial roads are shown to have largeKroad. The light blue polygons and the light orange polygons pinpoint the MDS for Hickey Blvd and E Hamilton Ave respectively. The white lines show the links that connect the selected road segment and its MDS. The two road segments have a similar traffic flow V ~400 (vehicles/hour), however, Hickey Blvd only has 12 MDS located nearby, whereas E Hamilton Ave has 51 MDS, not only located in the vicinity ofCampbell City, but also located in a few distant regions pinpointed by our methodology. (b) The degree distribution of driver sources can be approximated by a normal distribution with µsource = 1,035.9 (1,017.7), σsource = 792.2 (512.3), R2 = 0.78 (0.91) for Bay Area (Boston Area). (c) The degree distribution of road segments is approximated by a log-normal distribution  with µroad = 3.71 (3.36) , σroad = 0.82 (0.72), R2 = 0.98 (0.99) for Bay Area (Boston Area).

Notice that only when the traffic flow is greater than a road’s available capacity, the road is congested; the ratio of these two quantities is called Volume over Capacity (VOC) and defines the level of service of a road. Surprisingly, despite the different values in average flows v and average betweeness centrality β, we find the same distribution of VOC (Fig. 1c) in the two metropolitan areas, which follows an exponential distribution with an average VOC given by γ = 0.28 (R2>0.98):
The exponential decay of VOC indicates that for both road networks traffic flows on 98% of the road segments are well below their designed road capacities, whereas a few road segments suffer from congestion, having a VOC > 1. The similarity between the two VOC distributions shows that in both urbanities drivers experience the same level of service, due to utilizing the existing capacities in the similar way.
The traditional difficulty in gathering ODs at large scales has until now limited the comparison of roads in regard to their attractiveness for different driver sources. To capture the massive sources of daily road usage, for each road segment with V > 0, we calculate the fraction of traffic flow generated by each driver source, and rank these sources by their contribution to the traffic flow. Consequently, we define a road segment's major driver sources (MDS) as the top ranked sources that produce 80% of its traffic flow. We next define a bipartite network, which we call the network of road usage, formed by the edges connecting each road segment to their MDS. Hence, the degree of a driver source Ksource is the number of road segments for which the driver source is a MDS, and the degree of a road segment Kroad is the number of MDS that produce the vehicle flow in this road segment. As Fig. 2b shows, the driver source's degree Ksource is normally distributed, centered in < Ksource > ~1000 in both Bay Area and Boston Area, implying that drivers from each driver source use a similar number of road segments. In contrast, the road segment's degree Kroad follows a log-normal distribution (Fig. 2c), where most of the road segments have a degree centered in < Kroad > ~20. This indicates that the major usage of a road segment can be linked to surprisingly few driver sources. Indeed, only 6–7% of road segments are in the tail of the log-normal linked to a larger number of MDS, ranging from 100 to 300.
In Fig. 2a we show a road segment's degree Kroad in the road network maps of the Bay Area and the Boston Area. Since census tracts and mobile phone towers are designed to serve similar number of population , a road segment's degree Kroad quantifies the diversity of the drivers using it. We find that Kroad is lowly correlated with traditional measures, such as traffic flow,VOC and betweenness centrality bc . For example, in Fig. 2a, Hickey Blvd in Daly City and E Hamilton Ave in Campbell City have a similar traffic flow V~400 (vehicles/hour), however, their degrees in the network of road usage are rather different. Hickey Blvd, only has Kroad = 12, with MDS distributed nearby, whereas E Hamilton Ave, has Kroad = 51, with MDS distributed not only in its vicinity, but also in some distant areas as Palo Alto, Santa Cruz, Ben Lomond and Morgan Hill.
As Fig. 2a shows, the road segments in the tail of the log-normal (Kroad > 100) highlight both the highways and the major business districts in both regions. This again implies that Kroad can characterize a road segment's role in a transportation network associated with the usage diversity. To better characterize a road's functionality, we classify roads in four groups according to their bcand Kroad in the transportation network (Fig. 3). We define the connectors, as the road segments with the largest 25% of bc and the attractors as the road segments with the largest 25% of Kroad. The other two groups define the highways in the periphery, or peripheral connectors, and the majority of the roads are called local, which have both small bc and Kroad (Fig. 3). By combining bc and Kroad, a new quality in the understanding of urban road usage patterns can be achieved. Future models of distributed flows in urban road networks will benefit by incorporating those ubiquitous usage patterns.

Figure 3: Types of roads defined by bc and Kroad.

Types of roads defined by bc and Kroad.
The road segments are grouped by their betweenness centrality bc and degree Kroad. The red lines (connectors) represent the road segments with the top 25% of bc and Kroad; they are topologically important and diversely used by drivers. The green lines (peripheral connectors) represent the road segments in the top 25% of bc, but with low values of Kroad; they are topologically important, but less diversely used. The road segments in yellow are those with low values of bc, but within the top 25% Kroad; they behave as attractors to drivers from many sources (attractors). The road segments in grey have the low values of bc and Kroad, they are not topologically important and locally used (locals).


Today, as cities are growing at an unparalleled pace, particularly in Asia, South America and Africa, the power of this modeling framework is its ability to dynamically capture the massive sources of daily road usage based solely on mobile phone data and road network data, both of which are readily available in most cities. The values of Kroad and bc together determine a road's functionality. We find that the major traffic flows in congested roads are created by very few driver sources, which can be addressed by our finding that the major usage of most road segments can be linked to their own surprisingly few driver sources. This shows that the representation provided by the network of road usage is very powerful to create new applications, enabling cities to tailor targeted strategies to reduce the average daily travel time compared to a benchmark strategy.


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