Why urban heterogeneity limits the 15-minute city

Abstract

The `15-minute city' has emerged as a central paradigm in urban planning, promoting universal access to work and essential services within short travel times. Its feasibility-particularly for commuting to work-has however rarely been examined quantitatively. Here, we show that proximity to employment is fundamentally constrained by the internal structure of urban economies. Combining urban geometry with empirically observed firm-size distributions, we derive a lower bound on commuting times that holds independently of planning choices or transport technologies. This bound reveals a sharp transition: when employment is sufficiently concentrated, no spatial rearrangement of workplaces can ensure uniformly short commutes, even under optimal placement. Applied to Paris and its near suburbs, we find that achieving universal 15-minute commutes would require substantial economic restructuring or differentiated mobility strategies. The relevant question is therefore not whether an $x$-minute city is achievable, but what the minimal feasible $x$ is given a city's economic structure and spatial scale.

Figures (3)

• Figure 1: Comparison before and after optimization. Illustration of the simulated annealing optimization for a representative example ($E=1000$, $N=60$, $\gamma=1.5$, $m_1=424.6$, $m_N=1$). Firm locations are initially assigned at random (symbol size proportional to firm size), and workers are randomly allocated to firms. The initial configuration yields a maximal commuting distance $\ell_{\max}\approx1.69$. After simulated annealing ($T_{\mathrm{init}}=0.5$, $T_{\min}=10^{-4}$, $\alpha=0.95$, $n_{\mathrm{steps}}=1000$ per temperature), the system converges to an optimized spatial arrangement with $\ell_{\max}\approx 0.70$, corresponding to a reduction of $\sim 60\%$. In the optimized configuration, the largest firms are located closer to the center of the system, which reduces extreme commuting distances and prevents the occurrence of very long trips.
• Figure 2: Finite-size phase diagram of proximity feasibility. Optimized maximum commuting distance $\ell_{\max}$ as a function of the firm-size exponent $\gamma$, obtained from simulated annealing for a system with total employment $E=5000$, city radius $R=1$, establishment density $N=\alpha E$ with $\alpha=0.06$, and capacity tolerance $\delta=20\%$. Symbols show averages over $10$ independent spatial configurations. The dashed line indicates the theoretical lower bound $L_0^{\ast}$ given by Eq. \ref{['eq:fund']} for a uniform population density. Green and red shaded regions denote, respectively, feasible and infeasible proximity regimes: below the bound, no spatial arrangement of establishments can achieve a smaller maximum commuting distance, whereas above it realizable configurations exist.
• Figure 3: Theoretical minimum commuting time for Paris and its near suburbs. Minimal achievable commuting time $\tau_0(\gamma)$ as a function of the firm-size exponent $\gamma$, computed for the combined area of Paris and the petite couronne ($A=762~\mathrm{km}^2$). Solid curves correspond to walking ($v=5$ km/h) and dashed curves to cycling ($v=15$ km/h); colour encodes the number of establishments $N_{\rm est}$, with values $10^3$, $10^4$, $10^5$, $3\times10^5$, and $5\times10^5$. The shaded band beneath each curve shows the reduction in $\tau_0$ afforded by a capacity flexibility $\delta$ ranging from $0$ (upper edge) to $0.3$ (lower edge), corresponding to a multiplicative factor $\sqrt{1-\delta}$. The horizontal dotted line marks the 15-minute threshold, while the vertical dashed line indicates the empirical estimate $\hat{\gamma}\simeq1.38$.