Source-linked AI summary
Street Hierarchies: A Minority of Streets Account for a Majority of Traffic Flow
Bin Jiang
TL;DR
Urban streets exhibit a hierarchy in which a minority is structurally vital, but quantitative evidence linking this hierarchy to real traffic flow has been limited. Using geometric and topological analysis of Gävle’s street network alongside processed GPS taxi data, the paper finds that the highest-ranked streets carry most traffic. The top 20% account for 80% of traffic, while the top 1% account for more than 20%.
Problem
Quantitative evidence was limited on how urban street hierarchies operate geometrically, topologically, and in relation to real traffic flow.
Method
The paper analyzes Gävle’s street network through geometric and topological properties and compares the resulting hierarchies with processed GPS data from taxi cabs.
Results
The top 20% of streets account for 80% of traffic, while the top 1% account for more than 20%.
Takeaways & Limitations
Street hierarchy is a good indicator of traffic flow, with most traffic occurring on the top 20% of streets and nearly none on the bottom 20%.
Abstract
from arXiv · showhide
Urban streets are hierarchically organized in the sense that a majority of streets are trivial, while a minority of streets is vital. This hierarchy can be simply, but elegantly, characterized by the 80/20 principle, i.e. 80 percent of streets are less connected (below the average), while 20 percent of streets are well connected (above the average); out of the 20 percent, there is 1 percent of streets that are extremely well connected. This paper, using a European city as an example, examined, at a much more detailed level, such street hierarchies from the perspective of geometric and topological properties. Based on an empirical study, we further proved a previous conjecture that a minority of streets accounts for a majority of traffic flow; more accurately, the 20 percent of top streets accommodate 80 percent of traffic flow (20/80), and the 1 percent of top streets account for more than 20 percent of traffic flow (1/20). Our study provides new evidence as to how a city is (self-)organized, contributing to the understanding of cities and their evolution using increasingly available mobility geographic information.
1. Introduction
Urban streets form hierarchical networks in which most streets are less connected or smaller, while a minority is structurally vital. This paper examines those hierarchies through geometry, topology, and observed taxi-based traffic flow.
- 1. Introduction: Urban streets form connected network topologies rather than independent entities, enabling street hierarchies to be studied through their intersections.The connectivity graph represents streets as vertices and intersections as edges.
- 1. Introduction: 80% of streets are less connected than average, while 20% are more connected; the top 1% are extremely well connected.
- 1. Introduction: The paper examines street hierarchies at a detailed level through both geometric and topological properties.It also compares these hierarchies with traffic intensity measured from GPS-equipped taxi cabs.
- 1. Introduction: The study finds that street hierarchy conforms closely to observed traffic-flow intensity and provides evidence about how cities and their evolution are organized.
- 1. Introduction: The analysis proceeds from power-law characterization to Gävle’s geometric and topological hierarchies and then to traffic-flow distributions.
2. Power laws, Zipf’s law, and Pareto Distributions
Power laws describe highly uneven distributions in which many observations are small and few are large. The section introduces power-law, Zipf, and Pareto formulations and applies them to street-length hierarchies.
- Power-law distributions: A power law occurs when a value’s probability or frequency varies inversely as a power of that value.The formulation uses the quantity x and its probability p(x), with k and α as constants.
- Power-law distributions: Street-length distributions are highly right-skewed, with many shorter streets and relatively few longer streets.Figure 1 places street rank on the x axis and street length on the y axis.
- Zipf’s law: Zipf’s law models rank-size distributions through a probability distribution function, with x as rank and α close to 1.
- Pareto distributions: Pareto distributions describe the cumulative probability that a quantity exceeds x, distinguishing X > x from the point value X = x.
- Testing power laws: A straight line on a log-log plot is the standard signature used to examine whether a distribution follows a power law.In practice, power laws often include a cutoff at the smallest perceivable size rather than remaining linear across the full range.
3. Street hierarchies of Gävle city
Gävle’s street network exhibits hierarchical geometric and topological structure across natural and named streets. A small set of highly connected or central streets contrasts with a large majority of less prominent streets, forming four non-exclusive hierarchy levels.
- Network construction: Gävle’s analysis uses 1,292 natural streets and 1,002 named streets derived from the street network.Natural streets merge segments by continuity using a 60-degree deflection threshold; named streets dissolve segments sharing a name.
- Connectivity: 76.5% of natural streets have connectivity below the average value of 3.3.For named streets, the corresponding average connectivity is 3.5, although the supplied passage truncates the percentage below average.
- Street length: The top 20% of streets constitute about 60% of total street length, while the bottom 80% constitute about 40%.The bottom 20%—streets shorter than 100 meters—is included within the bottom 80%.
- Spatial hierarchy: Connectivity hierarchies map into spatial patterns with top 1%, remaining top 20%, and bottom 80% categories for both natural and named streets.The top 1% is shown in yellow, the rest of the top 20% in gray, and the bottom 80% in light gray.
- Betweenness: Betweenness centrality is highly right-skewed, with few streets having large values and many streets having small values.The rank-size plot’s falling part represents the bottom 80%, while the relatively flat part represents the top 20%.
- Scale structure: The network follows scale-free geometric and topological properties across four orders of scale, from 10-meter streets to 15- or 17-kilometer streets.Connectivity ranges from 1 to 49 for natural streets and from 1 to 59 for named streets; the four levels are top 1%, top 20%, bottom 80%, and bottom 20%.
4. Traffic distributions among the individual streets
The study combines taxi GPS data with street-network analysis to examine how traffic is distributed across named and natural streets. Traffic flow is strongly skewed: a minority of streets carries most observed traffic.
- Data source and processing: About 50 taxi cabs supplied GPS mobility data, recorded every ten seconds across Gävle and surrounding towns.The study focuses on Gävle, a city of about 70,000 inhabitants.
- Data source and processing: One week of cleaned GPS data was georeferenced to streets, adjusted for speed differences, and counted within 10-meter buffers to estimate street-use intensity.Approximately 100K locations were recorded daily.
- Observed traffic patterns: GPS traces showed that some downtown streets were intensively used while others had much lower traffic concentrations.The distribution was visualized through coordinate and trail density maps.
- Observed traffic patterns: Log-log plots showed a strikingly skewed flow distribution, with curves close to straight lines for individual streets.Natural streets displayed two parts with different slopes, indicating two regular categories.
- Hierarchical flow distribution: Top 20% of streets accounted for 80% of traffic, while the top 1% accounted for about 40% or 25% for natural and named streets, respectively.The bottom 80% accounted for about 15% and 20% of traffic for natural and named streets, respectively.
- Hierarchical flow distribution: The paper examined traffic across four non-exclusive hierarchical levels and concluded that street traffic follows an ordered hierarchy.The levels included top 10%, top 20%, bottom 80%, and bottom 20%.
5. Discussions on the related work
The discussion places street hierarchy within broader theories of hierarchical and scale-free organization in cities and complex networks. It interprets the observed street patterns as consistent with bottom-up self-organization across multiple scales.
- Theoretical interpretation: The paper treats street hierarchies as a verification of Salingaros’s multiplicity rule, described as a power law for urban street structure.The authors connect their findings to work by Alexander, Batty, Hillier, and Salingaros.
- Theoretical interpretation: The authors suggest that city and street hierarchies self-organize from the bottom up through local interactions rather than through top-down design.They describe hierarchy as operating from the smallest scales upward.
- Hierarchies across scales: Urban hierarchies extend beyond streets to cities within countries or regions, with many more small cities than large ones.The discussion relates these distributions to Zipf’s law and Pareto’s distribution.
- Complex-network context: Complex real-world networks commonly exhibit differentiated connectivity and hierarchical, scale-free structure.The discussion connects this perspective to research on small-world networks, scale-free networks, communities, and the Internet.
6. Conclusion
The conclusion finds ordered hierarchy in urban streets across geometry, topology, and observed traffic flow. It argues that street function follows street structure while emphasizing that all hierarchical levels remain important to urban life.
- Hierarchical structure: Distributions of geometric properties, topological properties, and individual-street traffic flow were all found to be strongly skewed.The paper identifies top 10%, top 20%, bottom 80%, and bottom 20% as four non-exclusive scales.
- Urban function: All hierarchical levels are considered essential: lower-level streets provide environmental access, while higher-level streets connect people to remote places.This conclusion is framed in terms of the network topology as a whole.
- Traffic hierarchy: A majority of traffic occurs on the top 20% of streets, while nearly no traffic occurs on the bottom 20%.The conclusion presents these groups as functionally differentiated levels within the street hierarchy.
- Traffic hierarchy: The top 1% of streets account for more than 20% of traffic, and the top 20% account for 80% of traffic.The conclusion describes this as precise empirical support for the minority-majority traffic-flow relationship.
- Planning implication: The authors suggest that redevelopment scenarios should not violate the observed scaling relationship between street hierarchy and traffic flow.They also present scaling law as a means to analyze urban street networks.