arXiv subjects

Junfang Tian

Publications and source records attributed to Junfang Tian.

At least 19 recordsLinked to original sources

arXiv2026

A Strictly Proper Scoring-Rule Theory for Calibrating Stochastic Car-Following Models

Problem definition: Fixed parameters and inputs in a stochastic simulator induce a distribution over complete trajectories, not one trajectory. Calibration must assess this distribution, including variability and temporal dependence, against observations. Yet stochastic car-following models are commonly calibrated with trajectory-error objectives inherited from deterministic modelling. Methodology/results: We establish a scoring-rule theory of stochastic calibration. Strict propriety requires the data-generating distribution to uniquely minimise expected score. MRMean-I, the average run-wise error, drives separable stochastic spread to zero; MRMean-II, the error of the ensemble-mean trajectory, cannot identify a parameter that changes only spread; and MRMin, the error of the closest simulated run, has a population target that changes with ensemble size. These results are confirmed for stochastic Intelligent Driver Model extensions with additive acceleration noise and random desired headway. We recommend exact maximum likelihood when the correct transition density is available; otherwise, an unbiased simulation-based estimator of a strictly proper score. The energy score meets this requirement and gives the best held-out distributional prediction among the evaluated simulation-based objectives, although both models retain too-narrow bands and miss persistent disturbances. Implications:Strict propriety separates a valid calibration target from parameter identifiability and model adequacy. The theory applies to vector-valued outputs from stochastic transportation simulators; the car-following experiments illustrate its scope.

stat.ME↗

arXiv2026

A Structured Framework for Calibrating Stochastic Car-Following Models: Data Adequacy, Parameter Sensitivity, and Objective Selection

Calibrating a stochastic car-following model is harder than its deterministic counterpart: the loss itself becomes a random variable, so a favorable random realization can be mistaken for a good parameter vector. This paper develops a structured framework for calibrating stochastic car-following models -- a completeness-controlled synthetic design, a corrected variance-based sensitivity analysis (VBSA), and the minimum-realization (MRMIN) calibration protocol -- across two structurally different stochastic mechanisms, QIDM and IDM2D. We test two claims from deterministic calibration -- that a small number of parameters, and the trajectory itself above all, dominates the sensitivity ranking, and that spacing calibration keeps dominating speed calibration once dynamics are stochastic -- and ask whether a model's noise term can be calibrated on its own. In a balanced synthetic experiment, driving-regime completeness has a mean total-effect index on par with the model's most influential parameter and roughly two orders of magnitude above pair identity, extending rather than reversing the deterministic finding on trajectory-identity dominance. Under MRMIN, calibrating only the noise parameter against a population-wide deterministic fit more than doubles median spacing error across 1644 NGSIM trajectories, but fitting the deterministic parameters per trajectory first and calibrating noise on top recovers it. Spacing calibration remains more cross-dimensionally robust than speed calibration on average, but the deterministic guarantee that this dominance can never reverse is violated in 19-26% of trajectories for both mechanisms. A multi-objective screen in relative-error space then favors joint spacing-speed goodness-of-fit functions over single-dimension spacing calibration. Deterministic calibration guarantees should therefore be re-tested, not assumed, once a model is stochastic.

physics.soc-ph↗

arXiv2026

Human adaptive variability stabilises collective traffic dynamics

Automated systems are often designed on the assumption that replacing human behavioural variability with precise, uniform algorithmic control improves collective performance. In automotive traffic, this principle underlies commercial adaptive cruise control (ACC). Using two large-scale human-driving experiments comprising 2.95 million car-following observations, a 25-vehicle platoon experiment and a controlled 11-driver protocol, cross-validated with 0.77 million observations from the NGSIM dataset and data from 22 production ACC systems, together with empirically calibrated ACC simulations, we show the opposite: rigid algorithmic uniformity creates systemic fragility. Commercial rule-based controllers amplify small local perturbations into severe stop-and-go waves, increasing fuel consumption and carbon emissions by approximately 2.7- to 5.0-fold across scenarios. Human-driven platoons, by contrast, progressively dissipate disturbances and maintain smoother flow. We identify the behavioural mechanism behind this advantage: human car-following does not follow a fixed proportional spacing rule. Drivers continuously reshape their time-headway distributions across speed regimes, exhibiting a non-monotonic shift from efficiency-oriented to risk-sensitive regulation. This speed-dependent variability generates nonlinear damping that suppresses the synchronisation and propagation of local errors. Our findings challenge the view that human variability is merely suboptimal noise to be eliminated. More broadly, they suggest that robust large-scale interactive AI systems should embed adaptive, human-inspired behavioural flexibility rather than rely on rigid uniformity.

physics.soc-ph↗

arXiv2026

The Moving Target of Urban Equity: Spatiotemporal Demand and Double Disadvantage in Hefei, China

Equitable access to essential urban services is a pillar of modern planning, yet most accessibility models rely strictly on static residential locations, ignoring how demand shifts throughout the daily loop. This study introduces a population-based, temporally differentiated framework to examine the resulting "moving target" of urban equity, focusing on medical facilities and green spaces in Hefei, China. Utilising large-scale mobile phone GPS data, we construct dynamic residential and workplace population exposure surfaces to capture shifting hourly demand. We then evaluate accessibility via network-based travel times paired with a novel per-capita provision metric that accounts for real-time demand competition. We define \textit{double disadvantage} as the co-occurrence of poor spatial accessibility and insufficient per-capita service availability. Counterintuitively, the results reveal that double-disadvantaged areas cluster primarily along the inner suburban belt rather than the remote periphery, where per-capita service provision remains relatively sufficient. Furthermore, temporal shifts drastically alter equity landscapes: daytime workplace concentrations intensely exacerbate demand competition in urban job centres. These findings demonstrate that urban inequality depends heavily on spatiotemporal population flows rather than just the fixed location of services. Ultimately, achieving true urban equity requires dynamic planning interventions that address time-varying demand rather than focusing solely on static, home-based metrics.

physics.soc-ph↗

arXiv2025

A Driving Regime-Embedded Deep Learning Framework for Modeling Intra-Driver Heterogeneity in Multi-Scale Car-Following Dynamics

A fundamental challenge in car-following modeling lies in accurately representing the multi-scale complexity of driving behaviors, particularly the intra-driver heterogeneity where a single driver's actions fluctuate dynamically under varying conditions. While existing models, both conventional and data-driven, address behavioral heterogeneity to some extent, they often emphasize inter-driver heterogeneity or rely on simplified assumptions, limiting their ability to capture the dynamic heterogeneity of a single driver under different driving conditions. To address this gap, we propose a novel data-driven car-following framework that systematically embeds discrete driving regimes (e.g., steady-state following, acceleration, cruising) into vehicular motion predictions. Leveraging high-resolution traffic trajectory datasets, the proposed hybrid deep learning architecture combines Gated Recurrent Units for discrete driving regime classification with Long Short-Term Memory networks for continuous kinematic prediction, unifying discrete decision-making processes and continuous vehicular dynamics to comprehensively represent inter- and intra-driver heterogeneity. Driving regimes are identified using a bottom-up segmentation algorithm and Dynamic Time Warping, ensuring robust characterization of behavioral states across diverse traffic scenarios. Comparative analyses demonstrate that the framework significantly reduces prediction errors for acceleration (maximum MSE improvement reached 58.47\%), speed, and spacing metrics while reproducing critical traffic phenomena, such as stop-and-go wave propagation and oscillatory dynamics.

cs.LG↗

arXiv2025

Twenty-Five Years of the Intelligent Driver Model: Foundations, Extensions, Applications, and Future Directions

The Intelligent Driver Model (IDM), proposed in 2000, has become a foundational tool in traffic flow modeling, renowned for its simplicity, computational efficiency, and ability to capture diverse traffic dynamics. Over the past 25 years, IDM has significantly advanced car-following theory and found extensive application in intelligent transportation systems, including driver assistance systems and autonomous vehicle control. However, IDM's deterministic framework and simplified assumptions face limitations in addressing real-world complexities such as stochastic variability, driver heterogeneity, and mixed traffic conditions. This paper provides a systematic review and critical reflection on IDM's theoretical foundations, academic influence, practical applications, and model extensions. While highlighting IDM's contributions, we emphasize the need to extend the model into a modular and extensible framework. Future directions include integrating stochastic elements, human behavioral insights, and hybrid modeling approaches that combine physics-based structures with data-driven methodologies. By reimagining IDM as a flexible modeling basis, this paper aims to inspire its continued development to meet the demands of intelligent, connected, and increasingly complex traffic systems.

physics.soc-ph↗

arXiv2023

Experimental features of emissions and fuel consumption in a car-following platoon

The paper investigates the features of emissions and fuel consumption (EFC) in a car-following (CF) platoon based on two experimental datasets. Four classical EFC models are employed and a universal concave growth pattern of the EFC along a platoon has been demonstrated. A general framework of coupling EFC and CF models is tested by calibrating and simulating three classical CF models. This work first demonstrates that, at vehicle-pair level, all models perform well on EFC prediction. The intelligent driver model outperforms the other CF models on calibration accuracy, but this is not true on EFC prediction. Second, at platoon level, the predicted EFC is nearly constant along the platoon which qualitatively differs from the experimental observation. The investigation highlights that accurate estimations at vehicle level may be insufficient for analysis at platoon level due to the significant role of oscillation growth and evolution in EFC estimation.

physics.soc-ph↗

arXiv2023

On the calibration of stochastic car following models

Recent experimental and empirical observations have demonstrated that stochasticity plays a critical role in car following (CF) dynamics. To reproduce the observations, quite a few stochastic CF models have been proposed. However, while calibrating the deterministic CF models is well investigated, studies on how to calibrate the stochastic models are lacking. Motivated by this fact, this paper aims to address this fundamental research gap. Firstly, the CF experiment under the same driving environment is conducted and analyzed. Based on the experimental results, we test two previous calibration methods, i.e., the method to minimize the Multiple Runs Mean (MRMean) error and the method of maximum likelihood estimation (MLE). Deficiencies of the two methods have been identified. Next, we propose a new method to minimize the Multiple Runs Minimum (MRMin) error. Calibration based on the experimental data and the synthetic data demonstrates that the new method outperforms the two previous methods. Furthermore, the mechanisms of different methods are explored from the perspective of error analysis. The analysis indicates that the new method can be regarded as a nested optimization model. The method separates the aleatoric errors caused by stochasticity from the epistemic error caused by parameters, and it is able to deal with the two kinds of errors effectively. Finally, we find that under the calibration framework of stochastic CF models, the calibrated parameter set using spacing as MoP may not always outperform that using velocity as MoP. These findings are expected to enhance the understanding of the role of stochasticity in CF dynamics where the new calibration framework for stochastic CF models is established.

physics.soc-ph↗

arXiv2022

Experimental study and modeling of the lower-level controller of automated vehicle

Accurate modeling of lower-level controller plays an important role in the traffic flow of automated vehicles (AVs). However, there lacks enough attention with this respect. To address this issue, we conduct a field experiment with two vehicles that are equipped with developable autonomous driving system, where one can customize the upper-level control algorithm. Based on the field experimental data, a new lower-level control model is developed and compared with two widely used ones. The comparison results show that the proposed model outperforms the two previous models in capturing the observed actual acceleration, especially the troughs of the acceleration time series. Furthermore, theoretical analysis indicates that comparing with the proposed model, the two previous models significantly overestimate the stability region of the traffic flow of the AVs and the capacity of stable traffic flow. Our study is expected to further shed light on the importance of accurate lower-level control modeling.

physics.soc-ph↗

arXiv2022

Oscillation growth in mixed traffic flow of human driven vehicles and automated vehicles: Experimental study and simulation

This paper reports an experimental study on oscillation growth in mixed traffic flow of automated vehicles (AVs) and human driven vehicles (HVs). The leading vehicle moves with constant speed in the experiment. The following vehicles consist of six developable AVs and different number of HVs. Thus, the market penetration rate (MPR) of AVs decreases with the increase of platoon size. The AVs are homogeneously distributed in the platoon. The constant time gap car-following policy is adopted for the AVs and the gap is set to 1.5 s. The experiment shows that in the 7-vehicle-platoon, the oscillations grow only slightly. In the 10-vehicle-platoon, the AVs could still significantly suppress the growth of oscillations. With the further decrease of MPR of AVs in the 13- and 20-vehicle-platoon, the AVs become having no significant impact on oscillation growth. On the other hand, with the decrease of MPR of AVs, average density of the vehicles and flow rate of the platoon increase, which demonstrates a trade-off between traffic stability and throughput under the given setup of AVs. The simulation study is also carried out, which exhibits good agreement with the experiment. Finally, sensitivity analysis of the parameters in the AV upper-level control algorithm has been performed, which is expected to guide future experiment design.

physics.soc-ph↗

arXiv2020

A comparison study on the growth pattern of traffic oscillations in car-following experiments

The evolution of oscillations is a very important issue in traffic flow studies. A recent car-following experiment (Experiment-I) showed that the speed standard deviation grows in a concave way along a platoon of vehicles following one another. This finding indicates that the traditional traffic instability mechanism is debatable, in which the speed standard deviation initially grows in a convex way. This paper has investigated the growth pattern of traffic oscillations in another car-following experiment (Experiment-II) and compared it with that in Experiment-I. It is shown that the speed standard deviation also exhibits concave growth characteristics in Experiment-II. The paired-sample t-test and the Mann-Kendall (MK) trend test showed that there is no significant difference between the two datasets. However, the acceleration standard deviation was remarkably larger in Experiment-II since drivers were asked to follow closely. Furthermore, a comparison experiment has been performed which indicates that the set of experiments on a circular track can be considered equivalent to that on a straight track. Our study is expected to shed light not only on traffic flow dynamics itself but also on the future design of the experiment scheme.

physics.soc-ph↗

arXiv2019

Car following behavioral stochasticity analysis and modelling: Perspective from wave travel time

This paper analyzes the car following behavioral stochasticity based on two sets of field experimental trajectory data by measuring the wave travel time series of vehicle n. The analysis shows that (i) No matter the speed of leading vehicle oscillates significantly or slightly, wave travel time might change significantly; (ii) A follower's wave travel time can vary from run to run even the leader travels at the same stable speed; (iii) Sometimes, even if the leader speed fluctuates significantly, the follower can keep a nearly constant value of wave travel time. The Augmented Dickey-Fuller test indicates that the time series the changing rate of wave travel time follows a mean reversion process, no matter the oscillations fully developed or not. Based on the finding, a simple stochastic Newell model is proposed. The concave growth pattern of traffic oscillations has been derived analytically. Furthermore, simulation results demonstrate that the new model well captures both macroscopic characteristic of traffic flow evolution and microscopic characteristic of car following.

nlin.AO↗

arXiv2018

On the role of speed adaptation and spacing indifference in traffic instability: evidence from car-following experiments and its stochastic modeling

Understanding the mechanisms responsible for the emergence and evolution of oscillations in traffic flow has been subject to intensive research by the traffic flow theory community. In our previous work, we proposed a new mechanism to explain the generation of traffic oscillations: traffic instability caused by the competition between speed adaptation and the cumulative effect of stochastic factors. In this paper, by conducting a closer examination of car following data obtained in a 25-car platoon experiment, we discovered that the speed difference plays a more important role on car-following dynamics than the spacing, and when its amplitude is small, the growth of oscillations is mainly determined by the stochastic factors that follow the mean reversion process; when its amplitude increases, the growth of the oscillations is determined by the competition between the stochastic factors and the speed difference. An explanation is then provided, based on the above findings, to why the speed variance in the oscillatory traffic grows in a concave way along the platoon. Finally, we proposed a mode-switching stochastic car-following model that incorporates the speed adaptation and spacing indifference behaviors of drivers, which captures the observed characteristics of oscillation and discharge rate. Sensitivity analysis shows that reaction delay only has slight effect but indifference region boundary has significant on oscillation growth rate and discharge rate.

physics.soc-ph↗

arXiv2018

Speed dependent stochasticity capacitates Newell model for synchronized flow and oscillation growth pattern

This paper has incorporated the stochasticity into the Newell car following model. Three stochastic driving factors have been considered: (i) Driver's acceleration is bounded. (ii) Driver's deceleration includes stochastic component, which is depicted by a deceleration with the randomization probability that is assumed to increase with the speed. (iii) Vehicles in the jam state have a larger randomization probability. Two simulation scenarios are conducted to test the model. In the first scenario, traffic flow on a circular road is investigated. In the second scenario, empirical traffic flow patterns in the NGSIM data induced by a rubberneck bottleneck is studied, and the simulated traffic oscillations and synchronized traffic flow are consistent with the empirical patterns. Moreover, two experiments of model calibration and validation are conducted. The first is to calibrate and validate using experimental data, which illustrates that the concave growth pattern has been quantitatively simulated. The second is to calibrate and cross validate vehicles' trajectories using NGSIM data, which exhibits that the car following behaviors of single vehicles can be well described. Therefore, our study highlights the importance of speed dependent stochasticity in traffic flow modeling, which cannot be ignored as in most car-following studies.

physics.soc-ph↗

arXiv2018

Theoretical investigation, simulation and empirical analysis of the growth pattern of traffic oscillations in the Euler coordinates

The formation and development of oscillations is an important traffic flow phenomenon. Recent studies found that along a vehicle platoon described in the Lagrangian specification, traffic oscillations grow in a concave way. Since stationary bottlenecks are more intuitively described in the Eulerian framework, this paper investigates whether the concave growth pattern of traffic oscillations in the Lagrangian coordinates can be transferred to the Euler coordinates (i.e. the concave increase in standard deviation is no longer measured across the vehicle indices but as a function of the road location). To this end, we theoretically unify these two ways of measuring oscillations by revealing their mapping relationship. We show that the growth pattern measured in the Lagrangian coordinates can be transferred to the Euler coordinates. We believe this finding is nontrivial since the scenarios are significantly different: while in vehicle platoons (Lagrangian view, non-penetrable moving bottleneck), the speed variance for a given vehicle is ideally constant, the drivers in the Eulerian setting (penetrable stationary bottleneck triggering the waves) experience all amplitudes, first the big ones and then the small ones. To test this proposition, we performed simulation using two different kinds of car-following models. Simulation results validate the theoretical analysis. Finally, we performed empirical analysis using the NGSIM data, which also validates the theoretical analysis.

nlin.PS↗

arXiv2018

Cellular automata approach to synchronized traffic flow modelling

Cellular automaton (CA) approach is an important theoretical framework for studying complex system behavior and has been widely applied in various research field. CA traffic flow models have the advantage of flexible evolution rules and high computation efficiency. Therefore, CA develops very quickly and has been widely applied in transportation field. In recent two decades, traffic flow study quickly developed, among which "synchronized flow" is perhaps one of the most important concepts and findings. Many new CA models have been proposed in this direction. This paper makes a review of development of CA models, concerning their ability to reproduce synchronized flow as well as traffic breakdown from free flow to synchronized flow. Finally, future directions have been discussed.

nlin.CG↗

arXiv2017

Car following model simulating traffic breakdown and concave growth pattern of oscillations in traffic flow

Traffic breakdown, as one of the most puzzling traffic flow phenomena, is characterized by sharply decreasing speed, abruptly increasing density and in particular suddenly plummeting capacity. In order to clarify its root mechanisms and model its observed properties, this paper proposes a car-following model based on the following assumptions: (i) There exists a preferred time-varied and speed-dependent space gap that cars hope to maintain; (ii) there exists a region R restricted by two critical space gaps and two critical speeds in the car following region on the speed-space gap diagram, in which cars' movements are determined by the weighted mean of the space- gap-determined acceleration and the speed-difference-determined acceleration; and (iii) out of region R, cars either accelerate to the free flow speed or decelerate to keep safety. Simulation results show that this model is able to simultaneously reproduce traffic breakdown and the transition from the synchronized traffic flow to wide moving jams. To our knowledge, this is the first car-following model that is able to fully depict traffic breakdown, spontaneous formation of jams, and the concave growth of the oscillations.

physics.soc-ph↗

arXiv2016

Empirical analysis and simulation of the evolution concavity of traffic oscillations

This paper has investigated the growth pattern of traffic oscillations in the NGSIM vehicle trajectories data, via measuring the standard deviation of vehicle velocity involved in oscillations. We found that the standard deviation of the velocity increases in a concave way along vehicles in the oscillations. Moreover, all datasets collapse into a single concave curve, which indicates a universal evolution law of oscillations. A comparison with traffic experiment shows that the empirical and the experimental results are highly compatible and can be fitted by a single concave curve, which demonstrates that qualitatively the growth pattern of oscillations is not affected by type of bottleneck and lane changing behavior. We have shown theoretically that small disturbances increase in a convex way in the initial stage in the traditional models presuming a unique relationship between speed and density, which obviously deviates from our findings. Simulations show that stochastic models in which the traffic state dynamically spans a 2D region in the speed-spacing plane can qualitatively or even quantitatively reproduce the concave growth pattern of traffic oscillations.

nlin.CG↗