Linear Models Match Machine Learning in Predicting Urban Bus Travel Times

Predictive modeling of bus travel time rates across four distinct mixed-traffic urban corridors in A Coruña, Spain, has demonstrated that traditional Multiple Linear Regression delivers predictive accuracy competitive with advanced machine learning techniques while preserving operational interpretability. In an empirical analysis leveraging more than forty-five million initial data points gathered from transit management logs, roadside Bluetooth sensors, and inductive loop detectors, researchers observed that none of the three evaluated machine learning algorithms—Artificial Neural Networks, Support Vector Regression, and Random Forest—consistently outperformed the others or demonstrated a substantial operational advantage over linear regression. This parity challenges common assumptions that complex non-linear architectures are automatically preferable for public transit operational forecasts.

Understanding and accurately quantifying the dynamic and static factors that determine bus travel times along congested urban arteries represents an enduring priority for transport authorities seeking to enhance transit attractiveness, especially for non-captive travelers who have alternative transportation choices. Buses operating in mixed traffic share rights-of-way with private automobiles, leaving transit vehicles directly vulnerable to surrounding road congestion, queuing delays at signalized intersections, and unexpected corridor bottlenecks. While early transit operational frameworks such as the Transit Capacity and Quality of Service Manual and the Highway Capacity Manual historically established that total bus delay stems from a combination of bus stop activities and running impedance along facilities, empirical modeling has frequently struggled to integrate high-resolution, empirical traffic data that coexists with individual bus journeys. Previous predictive efforts have frequently relied on static schedules, aggregated fifteen-minute traffic summaries, or time-of-day proxies rather than synchronized, minute-by-minute measurements of surrounding traffic streams, creating an empirical gap in capturing the simultaneous influence of dynamic road traffic, passenger boarding demands, and physical corridor configurations.

To overcome these historical limitations, the research team constructed an extensive multisource data pipeline capturing transit and vehicular movement throughout the first half of 2019, purposely selecting pre-pandemic conditions to avoid the behavioral anomalies and transit demand collapses caused by worldwide COVID-19 mobility disruptions. Data collection focused on four representative arterial corridors within A Coruña: Ronda de Outeiro, an outer ring road characterized by high population density and access to an industrial zone; Ronda de Nelle, an inner ring road traversing residential neighborhoods; Paseo Marítimo, a coastal promenade linking peripheral exit routes with the Old Town; and Avenida de Finisterre, a high-volume commercial and industrial conduit distinguished by having a substantial portion of its length restricted to a single mixed-traffic lane. The primary outcome variable was defined as the bus travel time rate expressed in seconds per kilometer, calculated by extracting the difference between vehicle arrival times at the first and last stops of each corridor across 18,530 individual bus runs recorded by the Compañía de Tranvías de La Coruña transit management system.

Dynamic explanatory variables were processed at unprecedented temporal and spatial resolutions to measure surrounding traffic conditions that coexisted with each individual transit journey. Inductive loop detectors embedded beneath street pavements captured traffic flow rates at one-minute intervals, which were mapped onto individual corridor segments termed vectors and averaged across the time windows during which buses traversed those specific roadway segments. Simultaneously, municipal roadside Bluetooth sensors recorded anonymized detections of active in-vehicle Bluetooth devices to establish general traffic travel times at three-minute intervals, which were aggregated across consecutive detector vectors to compute the corridor-level general traffic time rate in seconds per kilometer. Transit passenger activity was integrated using automated fare and dispatch databases that recorded passenger boardings across every corridor trip, yielding the average number of passenger boardings per stop. The authors specifically noted that passenger alightings could not be incorporated because regular urban bus systems in the study region do not monitor exit movements, requiring passenger activity to be represented through boarding totals.

In addition to dynamic metrics, the researchers introduced static infrastructure variables into a collective joint dataset pooling observations across all corridors to investigate structural effects and novel operational interactions. These static predictors included the number of bus stops per kilometer, the percentage of corridor length possessing only a single mixed-traffic lane, and the percentage of corridor length bordered by kerbside parking lanes. Notably, the study incorporated physical corridor characteristics as explicit interaction terms with dynamic variables, formulating an interaction between kerbside parking and traffic flow rates, alongside an interaction between single-lane roadway proportions and general traffic travel times. This interaction framework was designed to test whether physical constraints, such as curbside parking turnover or the absence of overtaking lanes, amplify the negative impacts of rising general traffic congestion on transit speeds, thereby creating an empirical planning tool capable of forecasting bus travel times in redesigned streets or newly planned corridors lacking prior bus service.

Model validation was carried out under a rigorous chronological train-test split designed to guarantee absolute temporal independence between training observations and evaluation outcomes. The first five months of chronological data served exclusively as the training corpus, while the final sixth month was reserved strictly as an unseen holdout test set, preventing temporal leakage that often artificially inflates random split evaluations. For machine learning architectures, hyperparameters were systematically tuned using cross-validation; Artificial Neural Networks were trained with a hyperbolic tangent activation function following standardized data normalization, Support Vector Regression models incorporated normalized features and an epsilon-insensitive loss tube, and Random Forest ensembles were tuned across tree quantities and split predictor subsets. Meanwhile, Multiple Linear Regression models were fitted via Ordinary Least Squares incorporating Heteroscedasticity and Autocorrelation Consistent standard errors to ensure reliable inferential statistics, accompanied by variance inflation factor calculations that verified the absence of harmful multicollinearity.

Evaluation of the corridor-specific models demonstrated comparable predictive capacity among the four methodologies, with each approach showing localized strengths rather than universal superiority across test sets. Support Vector Regression achieved the highest test coefficient of determination on Ronda de Outeiro and Ronda de Nelle, Random Forest achieved the highest test fit on Paseo Marítimo, and Multiple Linear Regression produced the superior test performance on Avenida de Finisterre. Overall, predictive accuracy was highest along Ronda de Outeiro and lowest on Avenida de Finisterre, where single-lane bottlenecks generated elevated travel times and higher dispersion. Multiple Linear Regression proved notably resilient, outperforming Artificial Neural Networks in three corridors, Random Forest in two corridors, and Support Vector Regression in one. While Random Forest generated markedly superior training fit metrics, this advantage deteriorated entirely on the unseen test data, demonstrating an underlying susceptibility to overfitting that was not mirrored by the simpler linear formulation.

Standardized regression coefficients extracted from the linear models revealed how transit operations and general traffic share responsibility for travel time variability. In Ronda de Outeiro, Ronda de Nelle, and Paseo Marítimo, precisely 50 percent of the explained variation in bus travel time rates was attributable to general traffic conditions, represented by traffic flow and general traffic travel times, while the remaining 50 percent stemmed directly from internal transit dynamics, represented by average passenger boardings per stop. In contrast, on the single-lane corridor of Avenida de Finisterre, traffic variables accounted for approximately two-thirds of the variation, leaving transit passenger activities responsible for only one-third. Across all individual corridors, an isolated increase of 60 seconds per kilometer in general traffic travel times increased bus travel time rates by 17.5 to 31.9 seconds per kilometer, representing an elevation of 6.83 to 9.78 percent above baseline speeds. Similarly, an increase of 100 vehicles per hour in traffic flow rate raised bus travel times by 7.8 to 20.0 seconds per kilometer, reflecting a 3.50 to 5.55 percent travel time increase.

The joint model incorporating both static corridor variables and interaction terms demonstrated exceptional explanatory capacity, elevating the test coefficient of determination to approximately 0.77 across all four modeling strategies. The maximum difference in test explanatory power among Artificial Neural Networks, Support Vector Regression, Multiple Linear Regression, and Random Forest was merely 0.01, indicating that independent variables explained nearly 77 percent of travel time variation regardless of the algorithmic engine employed. Artificial Neural Networks marginally led the joint test metrics, closely trailed by Support Vector Regression, Multiple Linear Regression, and Random Forest, with test error variations spanning less than 0.808 seconds per kilometer. The linear model demonstrated that adding one bus stop per kilometer increases bus travel time rates by 47.4 seconds per kilometer. Furthermore, if kerbside parking coverage increases by 10 percent, the marginal penalty of an additional 100 vehicles per hour surges from 12.4 to 28.3 seconds per kilometer, while an extra 10 percent of single-lane corridor length escalates the penalty of a 60-second general traffic slowdown from 23.8 to 32.5 seconds per kilometer.

In evaluating the broader implications and operational limitations of their work, the authors emphasized that the unexpected underperformance of neural network models in corridor-specific evaluations reflected the challenge of overlapping behavioral regimes within urban transit data. Neural networks excel at mapping recurring global patterns but tend to minimize broad error terms across conflicting regimes, such as peak versus off-peak hours and weekday versus holiday conditions, resulting in an averaging effect that smooths out granular travel time variations. The researchers acknowledged that their findings rely on rich urban sensor deployments that may not be available in all metropolitan areas, and noted that unrecorded factors such as passenger alightings and the limited total count of studied corridors necessitate cautious generalization. Nevertheless, because linear regression achieved predictive results essentially indistinguishable from complex machine learning while providing transparent coefficients for policy evaluation, the study concludes that simpler linear models remain the most practical and defensible tools for municipal transit planning, infrastructure redesign, and corridor prioritization under budgetary constraints.

Subject of Research: Comparative evaluation of predictive modeling strategies for urban bus travel times using multisource traffic data

Article Title: Bus travel time prediction in mixed traffic: a multisource big data approach with multiple modelling strategies

Article References: Montero-Lamas, Y., Fernandez, A., Gestal, M., Novales, M., & Orro, A. (2026). Bus travel time prediction in mixed traffic: a multisource big data approach with multiple modelling strategies. European Transport Research Review, 18(1), Article 57. https://doi.org/10.1186/s12544-026-00815-3

Image Credits: AI Generated

DOI: 10.1186/s12544-026-00815-3

Keywords: bus travel time prediction, mixed traffic conditions, multiple linear regression, support vector regression, artificial neural networks, random forest, urban corridor modeling, Bluetooth sensors, inductive loop detectors, A Coruña transit, traffic flow rate, general traffic time, passenger boardings, kerbside parking interaction, single lane congestion, transit planning analytics, dwell time delays