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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.

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., Comment: 34 pages, 13 figures, 17 tables

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.

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.

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.

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.

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.

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.

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., Comment: 15 pages, 10 figures

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.

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., Comment: 19 pages

This paper firstly show that 2 Dimensional Intelligent Driver Model (Jiang et al., PloS one, 9(4), e94351, 2014) is not able to replicate the synchronized traffic flow. Then we propose an improved model by considering the difference between the driving behaviors at high speeds and that at low speeds. Simulations show that the improved model can reproduce the phase transition from synchronized flow to wide moving jams, the spatiotemporal patterns of traffic flow induced by traffic bottleneck, and the evolution concavity of traffic oscillations (i.e. the standard deviation of the velocities of vehicles increases in a concave/linear way along the platoon). Validating results show that the empirical time series of traffic speed obtained from Floating Car Data can be well simulated as well., Comment: arXiv admin note: text overlap with arXiv:1507.04054

This paper has investigated the growth pattern of traffic oscillations by using vehicle trajectory data in a car following experiment. We measured the standard deviation of acceleration, emission and fuel consumption of each vehicle in the car-following platoon. We found that: (1) Similar to the standard deviation of speed, these indices exhibit a common feature of concave growth pattern along vehicles in the platoon; (2) The emission and fuel consumption of each vehicle decrease remarkably when the average speed of the platoon increases from low value; However, when reaches 30km/h, the change of emission and fuel consumption with is not so significant; (3), the correlations of emission and fuel consumption with both the standard deviation of acceleration and the speed oscillation are strong. Simulations show that with the memory effect of drivers taken into account, the improved two-dimensional intelligent driver model is able to reproduce the common feature of traffic oscillation evolution quite well.

This paper firstly show that a recent model (Tian et al., Transpn. Res. B 71, 138-157, 2015) is not able to well replicate the evolution concavity in traffic flow, i.e. the standard deviation of vehicles increases in a concave/linear way along the platoon. Then we propose an improved model by introducing the safe speed, the logistic function of the randomization probability, and small randomization deceleration for low-speed vehicles into the model. Simulations show that the improved model can well reproduce the metastable states, the spatiotemporal patterns, the phase transition behaviors of traffic flow, and the evolution concavity of traffic oscillations. Validating results show that the empirical time series of traffic speed obtained from Floating Car Data can be well simulated as well.

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.

This paper proposes an improved cellular automaton traffic flow model based on the brake light model, which takes into account that the desired time gap of vehicles is remarkably larger than one second. Although the hypothetical steady state of vehicles in the deterministic limit corresponds to a unique relationship between speeds and gaps in the proposed model, the traffic states of vehicles dynamically span a two-dimensional region in the plane of speed versus gap, due to the various randomizations. It is shown that the model is able to well reproduce (i) the free flow, synchronized flow, jam as well as the transitions among the three phases; (ii) the evolution features of disturbances and the spatiotemporal patterns in a car-following platoon; (iii) the empirical time series of traffic speed obtained from NGSIM data. Therefore, we argue that a model can potentially reproduce the empirical and experimental features of traffic flow, provided that the traffic states are able to dynamically span a 2D speed-gap region.

The essential distinction between the Fundamental Diagram Approach (FDA) and Kerner's Three- Phase Theory (KTPT) is the existence of a unique gap-speed (or flow-density) relationship in the former class. In order to verify this relationship, empirical data are analyzed with the following findings: (1) linear relationship between the actual space gap and speed can be identified when the speed difference between vehicles approximates zero; (2) vehicles accelerate or decelerate around the desired space gap most of the time. To explain these phenomena, we propose that, in congested traffic flow, the space gap between two vehicles will oscillate around the desired space gap in the deterministic limit. This assumption is formulated in terms of a cellular automaton. In contrast to FDA and KTPT, the new model does not have any congested steady-state solution. Simulations under periodic and open boundary conditions reproduce the empirical findings of KTPT. Calibrating and validating the model to detector data produces results that are better than that of previous studies., Comment: arXiv admin note: substantial text overlap with arXiv:1305.0680