A computational framework for quantifying route diversification in road networks

TL;DR

The paper tackles the problem of quantifying how road network structure enables route diversification beyond traditional congestion-focused metrics by introducing DiverCity, a measure that combines the number and spatial dispersion of near-shortest routes with respect to origin-destination pairs. Using a demand-free radial sampling approach, the authors compute $\\mathcal{D}(u,v) = \\mathcal{S}(\\text{NSR}(u,v)) \\cdot |\\text{NSR}(u,v)|$ where $\\mathcal{S}(\\text{NSR}) = 1 - J(\\text{NSR})$, across 56 global cities, uncovering systematic patterns: DiverCity generally increases with distance from the city center, declines near mobility attractors, and is higher in grid-like networks. They further show that speed-limit tuning on attractors can elevate city-wide DiverCity with modest travel-time costs, supported by controlled lattice simulations that reveal both local and global effects of attractors and bottlenecks. The work provides a practical framework for urban planners to balance route diversification, efficiency, and sustainability, and it offers an interactive platform for visualizing DiverCity distributions. The combination of a demand-free metric, scalable computation, and policy-relevant interventions makes DiverCity a valuable tool for planning resilient, adaptable urban mobility systems.

Abstract

The structure of road networks impacts various urban dynamics, from traffic congestion to environmental sustainability and access to essential services. Recent studies reveal that most roads are underutilized, faster alternative routes are often overlooked, and traffic is typically concentrated on a few corridors. In this article, we examine how road network structure, and in particular the presence of mobility attractors (e.g., highways and ring roads), shapes the counterpart to traffic concentration: route diversification. To this end, we introduce DiverCity, a measure that quantifies the extent to which traffic can potentially be distributed across multiple, loosely overlapping near-shortest routes. Analyzing 56 diverse global cities, we find that DiverCity is influenced by network characteristics and is associated with traffic efficiency. Within cities, DiverCity increases with distance from the city center before stabilizing in the periphery, but declines in the proximity of mobility attractors. We demonstrate that strategic speed limit adjustments on mobility attractors can increase DiverCity while preserving travel efficiency. We isolate the complex interplay between mobility attractors and DiverCity through simulations in a controlled setting, confirming the patterns observed in real-world cities. DiverCity provides a practical tool for urban planners and policymakers to optimize road network design and balance route diversification, efficiency, and sustainability. We provide an interactive platform (https://divercitymaps.github.io) to visualize the spatial distribution of DiverCity across all considered cities.

Figures (5)

• Figure 1: Overview of DiverCity and global patterns in urban road networks.(a) Example of a trip with low DiverCity (2.18) in Mumbai. Near-shortest routes significantly overlap, leading to low route diversity. (b) Example of a trip with high DiverCity (9) in Tokyo, characterized by multiple spatially diverse near-shortest routes. For panels (a) and (b), inset bar plots show the travel time of each alternative route, with NSRs in blue and non-feasible routes (exceeding the near-shortest threshold, shown as a dashed line) in red. (c) Distribution of median DiverCity across 56 cities, highlighting substantial variability. (d) DiverCity for trips at varying radial distances from the city center. The black line shows the global average, the light blue area represents the interquartile range, and the red line is an exponential fit ($R^2 = 0.93$). Deviations include Tokyo’s high values and Rome’s localized drop near its ring road. (e) Percentage of congested trips at different DiverCity values. The red line shows a linear fit ($R^2 = 0.96$), and the shaded area denotes the interquartile range across cities.
• Figure 2: DiverCity and mobility attractors.(a, b) Spatial distribution of node-level DiverCity, $\mathcal{D}(i)$, in Rome (a) and Tokyo (b). Values are interpolated between nodes, with mobility attractors highlighted in orange. Low-$\mathcal{D}(i)$ areas are represented in light blue, while high-$\mathcal{D}(i)$ areas are shown in dark blue, following the color gradient in the scale. Rome exhibits generally lower $\mathcal{D}(i)$ values and sparser attractors compared to Tokyo. In both cities, areas with low $\mathcal{D}(i)$ (relative to the city’s distribution) tend to cluster around mobility attractors. In Rome, low $\mathcal{D}(i)$ areas are strongly concentrated near the city's major ring road, while in Tokyo, they are distributed around branches of nearby mobility attractors, though less prominently than in Rome. (c) The average distance to the nearest attractor for nodes in different percentile ranges of $\mathcal{D}(i)$ within their respective cities. Nodes with lower $\mathcal{D}(i)$ are consistently closer to attractors. The dashed line represents the global average distance across all cities. (d) The relationship between city-level DiverCity ($\mathcal{D}_C$) and attractor density. Each point corresponds to a city, with color intensity indicating attractor spatial dispersion ($H$). Cities with denser and more evenly distributed attractors tend to have higher $\mathcal{D}_C$.
• Figure 3: Impact of speed limit tuning.(a) Effect of speed reductions on DiverCity. Cities such as Rome and Brussels show strong $\mathcal{D}_C$ improvements, while London follows the global trend with a peak at around 50% speed reduction before stabilizing. In contrast, Mumbai and Lagos exhibit limited or negative effects. (b) Effect of speed reductions on travel time. Cities with critical mobility bottlenecks (e.g., bridges in Rio de Janeiro, New York City, and San Francisco) experience disproportionately large increases in travel times beyond a 50% speed reduction. In panels (a) and (b), black lines represent the global average across all cities, while the blue shaded areas denote the interquartile range. (c-e) DiverCity for trips at varying radial distances for: (c) Lagos, where speed reductions negatively impact route diversification, (d) London, where DiverCity increases with speed reductions before stabilizing at 50% as the localized effect of attractors decreases, and (e) Rome, where reductions mitigate the localized dominance of mobility attractors such as the ring road. Speed reduction scenarios (in shades of red) are compared to the baseline case (black dashed line).
• Figure 4: Speed limit tuning in Rome. Traffic distribution in Rome under original speed limits (a) and after a 40% speed reduction (b). The width of each road segment is proportional to the number of near-shortest routes traversing it, based on the set of sampled trips $T$. Under original speed limits, routes are highly concentrated on the ring road, suppressing potential route diversity. After a 40% speed reduction, routes are more evenly distributed, reducing reliance on the ring road and enabling alternative routes to emerge. For each scenario, inset plots (1–3) focus on specific regions (highlighted in red on the map), providing magnified views of selected origin-destination pairs near and inside mobility attractor roads (shown in orange). The magnification factors are indicated in each inset. Under original speed limits (a), all alternative routes are funneled into the ring road, limiting route diversification. With speed reductions (b), fewer routes rely on the ring road, enabling alternative routes to emerge, increasing spatial diversity, and revealing previously "hidden" routes.
• Figure 5: Simulations in a controlled setting. (a) Illustration of the lattice grid model $L$, where intersections are represented as nodes and roads as edges. Thicker edges indicate mobility attractors with higher speed limits, while the remaining edges represent standard urban roads. (b) DiverCity, $\mathcal{D}(u, v)$, as a function of radial distance from the center of the lattice. Without mobility attractors, $\mathcal{D}(u, v)$ increases rapidly near the center and plateaus farther out, following a bounded exponential trend (red dashed line, $R^2 = 0.93$). (c) The average distance to the nearest attractor for nodes grouped by percentile ranges of $\mathcal{D}(i)$ in the lattice model. Nodes with lower $\mathcal{D}(i)$ are consistently closer to attractors, mirroring the trends observed in real-world road networks. (d) The effect of introducing attractors at varying distances from the center on $\mathcal{D}(u, v)$. A single attractor at 10 km sharply reduces $\mathcal{D}(u, v)$ near its location. Adding more attractors at greater distances (e.g., 10–12 km) helps stabilize and increase $\mathcal{D}(u, v)$ globally. (e) The effect of speed limit reductions on city-level DiverCity ($\mathcal{D}_C$) in the lattice. Reducing attractor speeds increases $\mathcal{D}_C$, with the largest improvements at around 50% speed reduction. Further reductions yield diminishing returns as attractors lose their dominance. (f) The impact of speed limit reductions on average travel time. For a simple lattice ($L$), travel time rises modestly with reductions. However, introducing a bridge-like bottleneck significantly amplifies travel time increases at higher speed reductions, reflecting the trend observed for real-world road networks.