Source-linked AI summary
Modeling car-following behavior on urban expressways in Shanghai: A naturalistic driving study
Meixin Zhu, Xuesong Wang, Andrew P. Tarko, Shou'en Fang
TL;DR
Existing car-following models were developed mainly from Western-country experiments, motivating evaluation for Shanghai drivers. Using naturalistic Shanghai driving data, the study calibrated, validated, and compared five models; IDM performed best, while drivers differed considerably and calibrated parameters were not numerically equivalent to observed ones.
Problem
Most car-following models were developed from Western-country experiments, motivating evaluation and possible adjustment for non-Western drivers in Shanghai.
Method
The study used Shanghai Naturalistic Driving Study data, extracting 2,100 urban expressway car-following periods to calibrate, validate, and cross-compare five car-following models.
Results
IDM had the lowest calibration and validation errors, while inter-driver spacing validation errors averaged 31% versus 19% for intra-driver errors.
Takeaways & Limitations
Model choice and calibration should account for driver differences, and calibrated parameters should not be assumed numerically equivalent to observable real-world parameters.
Takeaways & Limitations
The investigated models showed limitations for Shanghai drivers because observable parameters did not reliably replicate measured spacing and flow relationships.
Abstract
from arXiv · showhide
Five car-following models were calibrated, validated and cross-compared. The intelligent driver model performed best among the evaluated models. Considerable behavioral differences between different drivers were found. Calibrated model parameters may not be numerically equivalent with observed ones.
1. Introduction
Microscopic traffic simulations depend on car-following models, yet most model development has relied on Western driving data. This study uses naturalistic Shanghai data to compare five models for urban expressways.
- Car-following models are central to microscopic traffic simulation, and their performance affects simulation validity.
- Most car-following research has been based on Western experiments, although driving styles, vehicles, regulations, and cultures differ across countries.
- Models calibrated for Western drivers may perform poorly for drivers in developing countries because model assumptions reflect driving behavior.
- SH-NDS recorded high-resolution real-world driving from 60 Shanghai drivers covering 161,055 km between December 2012 and December 2015.
- The study uses Shanghai urban-expressway data to calibrate and cross-compare five models, seeking insight into Chinese driving behavior and a suitable Shanghai model.
2. Literature review
The literature covers several car-following model families and emphasizes naturalistic, driver-specific data for calibration. Calibration compares simulated and observed behavior through a performance measure, goodness of fit, and optimization algorithm.
- Car-following models describe how a following vehicle responds to a lead vehicle, including stimulus-based, safety-distance, desired-measures, optimal-velocity, and psycho-physical approaches.
- Calibration finds parameters that minimize differences between simulated and observed variables.
- Naturalistic driving data capture drivers’ natural behavior, complete trajectories, and individual characterization, addressing limitations of field-track and anonymous-road data.
- Calibration methodology comprises a measure of performance, goodness of fit, and optimization algorithm.
- Spacing, defined from the following vehicle’s front bumper to the lead vehicle’s rear bumper, can provide more efficient and robust calibration than commonly used measures.
- RMSPE measures relative differences between observed and simulated measures of performance.
- Downhill simplex, genetic algorithm, and OptQuest/Multistart are widely used optimization algorithms, with genetic algorithms able to avoid local minima through stochastic global search.
3. Car-following models investigated in this study
The study investigates five representative car-following models spanning major modeling traditions. Their formulations differ in the behavioral mechanisms and variables used to determine following-vehicle acceleration or speed.
- The evaluated models are Gazis-Herman-Rothery, Gipps, intelligent driver, full velocity difference, and Wiedemann.
- GHR model: The GHR model is a stimulus-based formulation in which following behavior depends on acceleration, speed difference, spacing, and reaction time.
- Gipps model: The Gipps model combines free-flow and car-following modes, selecting the lower resulting speed within a safety-distance framework.
- IDM: The IDM is a desired-measures model that considers desired speed and desired following distance.
- IDM: IDM desired spacing depends on speed, speed difference, maximum acceleration, comfortable deceleration, minimum standstill spacing, and desired time headway.
- FVD model: The FVD model combines a gap-dependent optimal-velocity term with a term accounting for velocity difference as a linear stimulus.
- Wiedemann model: Wiedemann models distinguish free-flow, approach, steady-state following, and critical braking regimes using psychological and physical driving behavior.
4. Data collection and preparation
The SH-NDS collected multimodal naturalistic driving data from Shanghai drivers, including vehicle dynamics, radar, GPS, and synchronized video. Car-following periods were algorithmically extracted, visually confirmed, and restricted to urban expressways.
- The SH-NDS was conducted by Tongji University, GM, and VTTI to study vehicle use, handling, and Chinese drivers’ safety awareness.
- Five instrumented GM light vehicles recorded data from 60 Shanghai drivers who traveled 161,055 km during the three-year study.
- The data-acquisition system recorded CAN data, acceleration, radar range and range rate, environmental variables, GPS, and four synchronized camera views.
- The cameras monitored the driver, forward roadway, rear roadway, and hand movements, with data collected at 10–50 Hz.
- Car-following periods were extracted through an iterative filter and then confirmed by analyst review of the corresponding video.
- Extraction required a stable radar target, range below 120 m, lateral distance below 2.5 m, and duration over 15 s.
- The urban-expressway analysis retained 42 drivers because they accounted for 97% of the relevant car-following periods.
5. Calibration and validation methodology
The study calibrated car-following models against observed inter-vehicle spacing using genetic optimization, synthetic-data testing, and driver-specific five-fold cross-validation. The procedure penalized collisions and evaluated transferability to held-out periods.
- Calibration minimized RMSPE between modeled and observed inter-vehicle spacing sampled at 10 Hz.Spacing was defined from the following vehicle’s front bumper to the lead vehicle’s rear bumper.
- A large crash penalty made parameter combinations producing simulated collisions unattractive to the optimization algorithm.The penalty reflected that no collisions occurred in the analyzed car-following periods.
- The forward Euler method updated vehicle speed and position with a 0.1 s time step, while negative speeds were set to zero.
- The genetic algorithm evolved parameter populations through fitness evaluation, crossover, and mutation until termination.Because the algorithm is stochastic, optimization was repeated 12 times per driver and the minimum-RMSPE solution was retained.
- Synthetic-data testing recovered parameters close to the generating values and produced a calibration error of 0.003.The authors therefore considered the calibration process capable of finding optimum parameters on actual data.
- Models were calibrated separately for each driver, supporting simulation with driver-specific behaviors rather than average-driver parameters.
- Five-fold cross-validation randomly divided each driver’s 50 car-following periods into five subsets, using four for calibration and one for validation per iteration.Calibration and validation errors were averaged across iterations; the supplied workflow figure depicts these iterations for one driver.
6. RESULTS AND ANALYSIS
Across 42 drivers and five cross-validation iterations, the IDM achieved the strongest overall calibration and validation performance among the evaluated models. Parameter values differed across models even when parameters had the same nominal meaning.
- The reported parameter estimates were aggregated across five cross-validation iterations and 42 drivers.
- Parameters with the same nominal meaning, such as reaction time, had different estimated values across models because parameter estimates depend on each model’s parameter set and optimization objective.
- In validation, the IDM performed best for both FV speed and spacing, while GHR performed worst during calibration and FVD and IDM performed best.
- The IDM had the smallest standard deviation of error in both calibration and validation, indicating the most stable error performance among the models.
- The Gipps and IDM models produced no collisions, whereas GHR, FVD, and Wiedemann 99 produced collisions, especially during validation.
- The IDM had the overall best performance, combining the lowest mean errors, smallest error standard deviations, and no collisions in calibration and validation.
7. Summary and discussion
Using 2,100 Shanghai urban-expressway car-following periods, the study calibrated, validated, and compared five models. IDM performed best overall, while driver heterogeneity and differences between calibrated and observed parameters shaped the interpretation of model suitability.
- Study design: 2,100 urban-expressway car-following periods from the SH-NDS database were used to calibrate and validate five models.The models were evaluated using calibration and validation errors.
- Validation: Validation errors ranged from 19% to 34%, increased relative to calibration, and included collisions, demonstrating the need for validation data.Calibration errors ranged from 19% to 25%.
- Model comparison: IDM achieved the lowest errors in both calibration and validation, with 19% error in each phase.Its performance supported suitability for describing sampled Shanghai drivers’ car-following behavior.
- Model comparison: Compared with Wiedemann, IDM had smaller validation-error variability and five rather than eleven parameters, supporting easier and more stable calibration.The comparison also indicated better performance in traffic situations absent from calibration.
- Driver heterogeneity: Inter-driver spacing validation error averaged 31%, versus 19% for intra-driver validation, and five collisions occurred during inter-driver validation.These results indicate considerable behavioral differences among drivers and support driver-specific behavior or archetypes in simulation.
- Parameter interpretation: Observed IDM parameters generally correlated with calibrated parameters but were usually higher, while observed parameters produced significantly larger spacing validation errors.The findings indicate that interpretable calibrated parameters are linked to, but not necessarily numerically equivalent with, observable parameters.
Appendices
The appendices describe the Wiedemann 99 model’s regime-based acceleration calculation and the criteria used to extract candidate car-following periods. They also summarize model parameters and the staged threshold-selection process.
- Wiedemann 99 model: The Wiedemann 99 model distinguishes free driving, closing in, following, and emergency braking using thresholds based on relative distance and speed.Acceleration is then calculated according to the identified driving regime.
- Appendix materials: Appendix figures illustrate the Wiedemann model’s driving regimes, acceleration calculation process, and parameter constraints and summaries.Table A.1 summarizes Wiedemann parameters, including their bounds and descriptive statistics.
- Wiedemann 99 model: The appendix formulates thresholds using following gaps, vehicle speeds, speed differences, approach perception, and desired-speed conditions.The listed parameters include perception thresholds, desired speed, maximum acceleration, and model parameters CC0 to CC9.
- Car-following extraction: Car-following extraction was defined in three steps, beginning with relatively loose criteria designed to avoid missing potential periods.Initial screening required the vehicles to share a lane, remain within 150 m, and follow for longer than 15 s.
- Car-following extraction: The final extraction criteria are summarized as following range below 120 m, following duration above 15 s, and an additional threshold below 2.5.The appendix presents these criteria in the final row of its summary table.
(2) Sample valid car-following periods
The study sampled valid car-following periods from initially extracted candidates by checking whether the subject vehicle’s speed and longitudinal position were influenced by the immediately preceding vehicle.
- Valid-period sampling: 155 valid car-following periods were sampled from potential periods identified during the initial extraction step.Validity was assessed using speed and position curves together with video materials.
- Valid-period sampling: Typical speed and position curves for car-following periods are presented as an illustration of the sampled driving situations.The figure accompanies the validation of whether the subject vehicle was influenced by the lead vehicle.
(3) Determine final criteria based on the sampled valid car-following periods
The study used the sampled periods’ parameter ranges and prior criteria to determine final extraction thresholds, then examined model-parameter estimates and empirical IDM parameter measures.
- Final extraction criteria: Final car-following extraction criteria were determined from the parameter ranges of sampled periods and criteria reported in previous studies.The parameter ranges are summarized in Table B.2, while the final criteria appear in the last row of Table B.1.
- Model parameter estimates: Cumulative distributions summarize parameter estimates separately for the GHR, Gipps, IDM, FVD, and Wiedemann 99 models.The appendix provides one distribution figure for each model.
- Empirical IDM parameters: The IDM’s six parameters were assigned intuitive driving-regime meanings, including desired speed for free driving and desired time headway for steady-state following.Other parameters represent standstill gap, maximum acceleration, comfortable deceleration, and the acceleration exponent.
- Empirical IDM parameters: Observed IDM parameters were estimated from behavior-specific data, such as free-driving events, steady-state car-following, standing traffic, and acceleration or deceleration rates.The acceleration exponent was assumed to be 4 because it cannot be measured directly.