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.Comment: 19 page

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

Improved 2D Intelligent Driver Model simulating synchronized flow and evolution concavity in traffic flow

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:1507.0405

Common feature of concave growth pattern of oscillations in terms of speed, acceleration, fuel consumption and emission in car following: experiment and modeling

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

Cellular automaton model with dynamical 2D speed-gap relation reproduces empirical and experimental features of traffic flow

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

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

Cellular automaton model simulating spatiotemporal patterns, phase transitions and evolution concavity in traffic flow

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

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

Microscopic driving theory with oscillatory congested states: model and empirical verification

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:1305.068

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