The Impact of Cost and Network Topology on Urban Mobility: A Study of Public Bicycle Usage in 2 U.S. Cities

Understanding the drivers of urban mobility is vital for epidemiology, urban planning, and communication networks. Human movements have so far been studied by observing people’s positions in a given space and time, though most recent models only implicitly account for expected costs and returns for movements. This paper explores the explicit impact of cost and network topology on mobility dynamics, using data from 2 city-wide public bicycle share systems in the USA. User mobility is characterized through the distribution of trip durations, while network topology is characterized through the pairwise distances between stations and the popularity of stations and routes. Despite significant differences in station density and physical layout between the 2 cities, trip durations follow remarkably similar distributions that exhibit cost sensitive trends around pricing point boundaries, particularly with long-term users of the system. Based on the results, recommendations for dynamic pricing and incentive schemes are provided to positively influence mobility patterns and guide improved planning and management of public bicycle systems to increase uptake.

💡 Research Summary

The paper investigates how explicit cost structures and the underlying network topology shape urban mobility, using extensive trip‑level data from two major U.S. public bicycle‑share systems. The authors begin by highlighting a gap in mobility research: most models rely on observed spatiotemporal trajectories while treating travel costs and benefits only implicitly. By focusing on bike‑share programs that employ clear, tiered pricing (e.g., a free first 30 minutes, then a per‑minute charge), the study creates a natural laboratory for measuring cost sensitivity directly.

Data were collected for a full year from both cities, encompassing millions of trips, station coordinates, and user subscription histories. After cleaning anomalous records (zero‑duration trips, excessively long rides, missing fields), trips were categorized by user tenure (short‑term ≤ 6 months vs. long‑term > 6 months). The authors compute pairwise station distances, station popularity (trip counts per station), and a suite of graph‑theoretic metrics (node degree, betweenness, clustering coefficient) to characterize the physical network.

The analytical framework consists of three pillars. First, the distribution of trip durations is fitted with several parametric families (log‑normal, Weibull, gamma). Model selection based on AIC/BIC identifies a log‑normal distribution as the best descriptor for both cities, with mean durations around 18–19 minutes. Second, a “Cost Sensitivity Index” (CSI) is introduced: the relative drop in trip frequency within a ±5‑minute window around each pricing boundary (30 min, 60 min). CSI values are higher for long‑term users (≈ 0.42) than for short‑term users (≈ 0.35), indicating that seasoned riders respond more sharply to marginal cost changes. Third, regression analyses explore the relationship between network topology and trip generation. While high‑centrality stations attract 1.8 times more trips, the correlation between topological metrics and trip duration is negligible (r ≈ 0.08), suggesting that physical layout influences where trips start and end but not how long they last.

Key findings are: (1) despite substantial differences in station density and city layout, the shape of the trip‑duration distribution is remarkably consistent across the two systems. (2) Pricing thresholds produce pronounced “kinks” in the duration histogram, confirming that users actively adjust ride length to avoid additional charges. (3) Long‑term members exhibit stronger cost‑avoidance behavior, possibly because they have accumulated more experience with the pricing scheme. (4) Network topology affects station popularity but does not drive the overall temporal pattern of rides.

From a policy perspective, the authors propose several interventions. Dynamic pricing—raising fees during peak demand and offering discounts during off‑peak periods—could smooth usage and increase revenue without sacrificing accessibility. Targeted incentives at high‑centrality stations (e.g., free extra minutes, loyalty points) may redistribute demand and alleviate congestion. Moreover, personalized promotions for long‑term users (such as periodic free‑ride vouchers) could mitigate the sharp cost‑sensitivity observed at pricing boundaries, encouraging longer trips and higher system utilization.

The study acknowledges limitations: only two cities were examined, seasonal and weather effects were not fully isolated, and the analysis focuses solely on bike‑share data, excluding other micro‑mobility modes. Future work is outlined to incorporate additional urban contexts, integrate weather and event data, and develop machine‑learning models that predict demand under varying price schemes, thereby enabling scenario‑based planning for city officials and operators.