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• A classification for string stability is proposed to reconcile approaches from different fields. • We show equivalence between asymptotic and L 2 string stability of car-following models. • The only available condition for car-following string stability of a heterogeneous flow is proven inaccurate. • Uncertain transfer functions are proposed to study the string stability of a mixed and heterogenous traffic. • We shift from the study of the stability of a model, to the study of the stability of a traffic flow. Urged by a close future perspective of a traffic flow made of a mix of human-driven vehicles and connected, automated vehicles (CAVs), research has recently focused at making the most of CAVs capabilities to mitigate the instability of the whole, i.e. mixed , traffic flow. In all works, however, either the two sub-flows are studied under a simplifying but unrealistic assumption of flow homogeneity , or drivers' and vehicles heterogeneity is not correctly taken into account within each sub-flow. We show here that the only condition developed so far to study a car-following model string stability for a heterogeneous flow, is inaccurate. Therefore, we propose a methodology to model string stability that considers drivers' and vehicles heterogeneity , which is the essence of a real traffic. Uncertain transfer functions are introduced to map the probability distributions of car-following model parameters into a L 2 stability measure of a mixed and heterogeneous traffic. Specifically, they allow us to move from the stability analysis of a car-following model , or of a controller , to the stability analysis of a traffic flow , as interpreted by that model, or controller. Eventually, several other theoretical contributions on stability analysis are given in the paper, aiming at reconciling approaches from different fields. Among these, a mathematical justification of the equivalence between the asymptotic stability of a closed-loop platoon system – which has been studied through the famous "traffic wave ansatz" on a ring-road – and the L 2 stability of an open-loop platoon system. [ABSTRACT FROM AUTHOR]

Highlights • Algorithm for calibration of car-following model for large-scale microscopic network models. • City-scale case study is carried out, the approach is shown to be computationally efficient and suitable for large-scale network models. • Compared to a traditional approach, it improves the objective function by two orders of magnitude and it improves the fit to link speeds by one order of magnitude. Abstract This paper proposes a simulation-based optimization methodology for the efficient calibration of microscopic traffic flow models (i.e., car-following models) of large-scale stochastic network simulators. The approach is a metamodel simulation-based optimization (SO) method. To improve computational efficiency of the SO algorithm, problem-specific and simulator-specific structural information is embedded into a metamodel. As a closed-form expression is sought, we propose adopting the steady-state solution of the car-following model as an approximation of its simulation-based input-output mapping. This general approach is applied for the calibration of the Gipps car-following model embedded in a microscopic traffic network simulator, on a large network. To this end, a novel formulation for the traffic stream models corresponding to the Gipps car-following law is provided. The proposed approach identifies points with good performance within few simulation runs. Comparing its performances to that of a traditional approach, which does not take advantage of the structural information, the objective function is improved by two orders of magnitude in most experiments. Moreover, this is achieved within tight computational budgets, i.e., few simulation runs. The solutions identified improve the fit to the field measurements by one order of magnitude, on average. The structural information provided to the metamodel is shown to enable the SO algorithm to become robust to both the quality of the initial points and the simulator stochasticity. [ABSTRACT FROM AUTHOR]

This paper proves that in traffic flow model calibration and validation the cumulative sum of a variable has to be preferred to the variable itself as a measure of performance. As shown through analytical relationships, model residuals dynamics are preserved if discrepancy measures of a model against reality are calculated on a cumulative variable, rather than on the variable itself. Keeping memory of model residuals occurrence times is essential in traffic flow modelling where the ability of reproducing the dynamics of a phenomenon – as a bottleneck evolution or a vehicle deceleration profile – may count as much as the ability of reproducing its order of magnitude. According to the aforesaid finding, in a car-following models context, calibration on travelled space is more robust than calibration on speed or acceleration. Similarly in case of macroscopic traffic flow models validation and calibration, cumulative flows are to be preferred to flows. Actually, the findings above hold for any dynamic model. [ABSTRACT FROM AUTHOR]

Abstract: Trajectories drawn in a common reference system by all the vehicles on a road are the ultimate empirical data to investigate traffic dynamics. The vast amount of such data made freely available by the Next Generation SIMulation (NGSIM) program is therefore opening up new horizons in studying traffic flow theory. Yet the quality of trajectory data and its impact on the reliability of related studies was a vastly underestimated problem in the traffic literature even before the availability of NGSIM data. The absence of established methods to assess data accuracy and even of a common understanding of the problem makes it hard to speak of reproducibility of experiments and objective comparison of results, in particular in a research field where the complexity of human behaviour is an intrinsic challenge to the scientific method. Therefore this paper intends to design quantitative methods to inspect trajectory data. To this aim first the structure of the error on point measurements and its propagation on the space travelled are investigated. Analytical evidence of the bias propagated in the vehicle trajectory functions and a related consistency requirement are given. Literature on estimation/filtering techniques is then reviewed in light of this requirement and a number of error statistics suitable to inspect trajectory data are proposed. The designed methodology, involving jerk analysis, consistency analysis and spectral analysis, is then applied to the complete set of NGSIM databases. [Copyright &y& Elsevier]

• Heterogeneity of drivers and vehicles makes platoons more unstable, on average. • L ∞ characterization of string stability is more appropriate than L 2 one. • Analytical sufficient condition for L ∞ string stability is derived. • L p norm variability due to platoon length, speed, and parameters pdfs is analysed. • Parameters pdfs shape and correlation sensibly affect string stability. This paper shows that the heterogeneity of drivers' and vehicles characteristics makes platoons, on average, more string-unstable. However, the string instability degree of unstable platoons is much higher in a homogeneous flow than in a heterogeneous one. These results are based on an L ∞ characterization of string stability, which is shown to be the most appropriate one from a traffic safety viewpoint. Mechanisms and conditions are discussed in which an L 2 characterization is not able to capture the amplification of a speed drop through a string of vehicles. An analytical sufficient condition for the L ∞ string stability of heterogeneous vehicles, which move according to a general class of car-following models, is derived. Above all, a thorough comparison of L ∞ and L 2 string stability characterizations between a homogeneous and a heterogenous flow, is performed. To this aim, the L p norms of heterogeneous platoons are calculated within a quasi-Monte Carlo framework. The variability of the L p norm values due to the platoon length, the equilibrium speed, and the probability distribution model of the uncertain vehicle parameters, is analysed. Overall, it is shown that the platoon stability behaviour sensibly changes with the shape and the correlation structure of vehicle model parameter distributions. Therefore, traffic heterogeneity needs to be modelled in order to correctly characterize the string stability of a mixed traffic flow. [ABSTRACT FROM AUTHOR]

Estimation/updating of Origin–Destination (OD) flows and other traffic state parameters is a classical, widely adopted procedure in transport engineering, both in off-line and in on-line contexts. Notwithstanding numerous approaches proposed in the literature, there is still room for considerable improvements, also leveraging the unprecedented opportunity offered by information and communication technologies and big data. A key issue relates to the unobservability of OD flows in real networks – except from closed highway systems – thus leading to inherent difficulties in measuring performance of OD flows estimation/updating methods and algorithms. Starting from these premises, the paper proposes a common evaluation and benchmarking framework, providing a synthetic test bed, which enables implementation and comparison of OD estimation/updating algorithms and methodologies under “standardized” conditions. The framework, implemented in a platform available to interested parties upon request, has been flexibly designed and allows comparing a variety of approaches under various settings and conditions. Specifically, the structure and the key features of the framework are presented, along with a detailed experimental design for the application of different dynamic OD flow estimation algorithms. By way of example, applications to both off-line/planning and on-line algorithms are presented, together with a demonstration of the extensibility of the presented framework to accommodate additional data sources. [ABSTRACT FROM AUTHOR]

Fuel consumption or pollutant emissions can be assessed by coupling a microscopic traffic flow model with an instantaneous emission model. Traffic models are usually calibrated using goodness of fit indicators related to the traffic behavior. Thus, this paper investigates how such a calibration influences the accuracy of fuel consumption and NOx and PM estimations. Two traffic models are investigated: Newell and Gipps. It appears that the Gipps model provides the closest simulated trajectories when compared to real ones. Interestingly, a reverse ranking is observed for fuel consumption, NOx and PM emissions. For both models, the emissions of single vehicles are very sensitive to the calibration. This is confirmed by a global sensitivity analysis of the Gipps model that shows that non-optimal parameters significantly increase the variance of the outputs. Fortunately, this is no longer the case when emissions are calculated for a group of many vehicles. Indeed, the mean errors for platoons are close to 10% for the Gipps model and always lower than 4% for the Newell model. Another interesting property is that optimal parameters for each vehicle can be replaced by the mean values with no discrepancy for the Newell model and low discrepancies for the Gipps model when calculating the different emission outputs. Finally, this study presents preliminary results that show that multi-objective calibration methods are certainly the best direction for future works on the Gipps model. Indeed, the accuracy of vehicle emissions can be highly improved with negligible counterparts on the traffic model accuracy. [ABSTRACT FROM AUTHOR]

• Accuracy of ninety CF models and ACC algorithms is compared. • New controllers with spacing policies from the IDM and Gipps' models are studied. • The impact on accuracy of increasingly complex lower-level dynamics is evaluated. • The linear controller with Gipps' spacing policy is the most accurate model. • The IDM is the most robust model, also showing zero crashes in cross-validation. This paper investigates the accuracy and robustness of car-following (CF) and adaptive cruise control (ACC) models in reproducing measured trajectories of commercial ACCs. To this aim, a general modelling framework is proposed, in which ACC and CF models have been incrementally augmented with physics-based extensions: namely, perception delay, linear or nonlinear vehicle dynamics, and acceleration constraints. This framework has been applied to the Intelligent Driver Model (IDM), Gipps' model, and to three basic ACC algorithms. These are linear controllers which are coupled with a constant time-headway spacing policy, and with two other policies derived from the traffic flow theory: the IDM desired distance function, and Gipps' equilibrium distance-speed function. The ninety models resulting from the combination of the five base models with the aforementioned extensions, have been assessed and compared through a vast calibration and validation experiment against measured trajectory data of vehicles driven by ACC systems. Overall, the study has shown that physics-based extensions provide limited improvements to the accuracy of existing models. In addition, if an investigation against measured data is not carried out, it is not possible to argue which extension is the most suited for a specific model. The linear controller with Gipps' spacing policy has resulted the most accurate model, while the IDM the most robust to different input trajectories. Eventually, all models have failed to capture the behaviour of some car brands – just as models fail with some human drivers. Therefore, the choice of the "best" model is independent of the car brand to simulate. [ABSTRACT FROM AUTHOR]