Evolution Process Of Traffic Flow Research Articles

Modeling and simulation of traffic flow based on memory effect and driver characteristics

In this paper, an improvement of the full velocity difference model is presented, which comprehensively considers driver characteristics which include aggressive and timid behaviors and memory effect. The stability condition of the improved model is obtained by making use of the small perturbation method. The Burgers, Korteweg–de Vries and modified Korteweg–de Vries equations are derived by means of the reductive perturbation method. Finally, through numerical simulation, the traffic flow evolution process of the improved model under two typical conditions is observed. The first is the starting process, and the second is the propagation process of disturbance in traffic flow. The results of numerical simulation and theoretical analysis demonstrate that the multiple driver characteristics considered in the improved model have important influences on traffic flow stability and the ease of traffic jams, and the model can quickly recover to its original state in case of the disturbance. • A new car following model is presented, which considers memory effect and driver characteristics including aggressive and timid behaviors. • The stability conditions of the extended model are obtained with the use of the small perturbation method. • The Burgers, Korteweg–de Vries and modified Korteweg–de Vries equations are derived by means of the reduced perturbation method. • The starting process and the propagation process of disturbance are carried out, the results are much closer to actual traffic.

Dynamic Assessment of Road Network Vulnerability Based on Cell Transmission Model

The road network maintaining stability is critical for guaranteeing urban traffic function. Therefore, the vulnerable links need to be identified accurately. Previous vulnerability research under static condition compared the operating states of the old equilibrium before the event and the new equilibrium after the event to assess vulnerability ignoring the dynamic variation process. Does road network vulnerability change over time? This paper combines the vulnerability assessment with the traffic flow evolution process, exploring the road network vulnerability evaluation from the perspective of time dimension. More accurate identification and evaluation of vulnerable nodes and links can help to strengthen the ability of road network resisting disturbances. A modified dynamic traffic assignment (DTA) model is established for dynamic path selection (reselect the shortest path at the end of each link) based on the dynamic user optimal (DUO) principle. A modified cell transmission model is established to simulate the traffic flow evolution processes. The cumulative and time-varying index of vulnerability assessment is established from the viewpoint of traveler’s time loss. Then the road network vulnerability assessment combined the traffic flow model with the vulnerability index. The road network vulnerability assessment of Bao’an Central District of Shenzhen, China, reveals that road network vulnerability does contain a dynamic process, and vulnerable links in each phase can be exactly identified by the model. Results showed that the road network would have a large vulnerability during the disordered phase when the main road fails. Therefore, prioritizing the smooth flow of main roads can weaken the impact of road network vulnerability exposure.

A Traffic Flow Evolution Process toward Mixed Equilibrium with Multicriteria of Route Choice Behaviour

Based on the price-quantity adjustment behaviour principle of disequilibrium theory, the route choices of travellers are also affected by a quantity signal known as traffic flow, while the route cost is considered as a price signal in economics. Considering the quantity signal’s effect among travellers, a new route comfort choice behaviour criterion and its corresponding equilibrium condition are established. The network travellers are classified into three groups according to their route choice behaviour: travellers in the first group choose the shortest route following the route rapidity behaviour criterion with complete information forming the UE (user equilibrium) pattern, travellers in the second group choose the most comfortable route following the route comfort behaviour criterion with complete information forming the QUE (quantity adjustment user equilibrium) pattern, and travellers in the third group choose a route according to their perceived travel time with incomplete information forming the SUE (stochastic user equilibrium) pattern. The traffic flows of all three groups converge to a new UE-QUE-SUE mixed equilibrium flow pattern after interaction. To depict the traveller-diversified choice behaviour and the traffic flow interaction process, a mixed equilibrium traffic flow evolution model is formulated. After defining the route comfort indicator and the corresponding user equilibrium state, the equilibrium conditions of the three group flows are given under a mixed equilibrium pattern. In addition, an equivalent mathematical programming of the mixed equilibrium traffic flow evolution model is proposed to demonstrate that the developed model converges to the mixed equilibrium state. Finally, numerical examples are examined to evaluate the effect of route comfort proportions on the traffic network flow evolution and analyse the performance of the proposed model.

A Markov Traffic Model for Signalized Traffic Networks Based on Bayesian Estimation

In order to better understand the stochastic dynamic features of signalized traffic networks, we propose a Markov traffic model to simulate the dynamics of traffic link flow density for signalized urban traffic networks with demand uncertainty. In this model, we have four different state modes for the link according to different congestion levels of the link. Each link can only be in one of the four link state modes at any time, and the transition probability from one state to the other state is estimated by Bayesian estimation based on the distributions of the dynamic traffic flow densities, and the posterior probabilities. Therefore, we use a first-order Markov Chain Model to describe the dynamics of the traffic flow evolution process. We illustrate our approach for a small traffic network. Compared with the data from the microscopic traffic simulator SUMO, the proposed model can estimate the link traffic densities accurately and can give a reliable estimation of the uncertainties in the dynamic process of signalized traffic networks.

Discrete-time dynamic road congestion pricing under stochastic user optimal principle

Road pricing is believed to be an effective instrument for alleviating roadway congestion. Most existing road pricing schemes are developed based on traditional static traffic equilibrium models, in which a fixed toll can be obtained to support the corresponding traffic flow pattern as an equilibrium. However, static models cannot consider the evolution process of traffic flow caused by the day-to-day fluctuations of road users’ route choices. Under practical traffic conditions, the multiple traffic equilibria may exist (e.g., due to the asymmetric travel cost function). Indeed, the fixed road pricing scheme derived from the equilibrium model cannot guarantee that the dynamic traffic system can converge to the desired equilibrium state from any initial traffic state. This study, assuming that travelers follow the stochastic user optimal principle, develops a day-to-day dynamic road pricing scheme that can drive the traffic dynamic system to converge to a given stochastic user equilibrium (SUE) even when the traffic system has multiple SUE states. The characteristic of this dynamic road pricing scheme is verified by rigorous proof and numerical tests in this study.

Distance-Based Congestion Pricing with Day-to-Day Dynamic Traffic Flow Evolution Process

This paper studies the distance-based congestion pricing in a network considering the day-to-day dynamic traffic flow evolution process. It is well known that, after an implementation or adjustment of a new congestion toll scheme, the network environment will change and traffic flows will be nonequilibrium in the following days; thus it is not suitable to take the equilibrium-based indexes as the objective of the congestion toll. In the context of nonequilibrium state, prior research proposed a mini–max regret model to solve the distance-based congestion pricing problem in a network considering day-to-day dynamics. However, it is computationally demanding due to the calculation of minimal total travel cost for each day among the whole planning horizon. Therefore, in order to overcome the expensive computational burden problem and make the robust toll scheme more practical, we propose a new robust optimization model in this paper. The essence of this model, which is an extension of our prior work, is to optimize the worst condition among the whole planning period and ameliorate severe traffic congestions in some bad days. Firstly, a piecewise linear function is adopted to formulate the nonlinear distance toll, which can be encapsulated to a day-to-day dynamics context. A very clear and concise model named logit-type Markov adaptive learning model is then proposed to depict commuters’ day-to-day route choice behaviors. Finally, a robust optimization model which minimizes the maximum total travel cost among the whole planning horizon is formulated and a modified artificial bee colony algorithm is developed for the robust optimization model.

Effects of the prevision relative velocity on traffic dynamics in the ACC strategy

This paper focuses on exploring the effects of the prevision relative velocity on the dynamics characteristic of the simulated traffic flow in the ACC strategy. Firstly, an improved car-following considering the prevision relative velocity is developed for numerical simulations. Secondly, an adaptive neural-fuzzy inference system is trained and employed to predict the relative velocity. Thirdly, a microscopic traffic simulation program is created to analyze the traffic flow evolution process, further to explore the effects of the prevision relative velocity on the dynamics characteristic. The results show that considering the prevision relative velocity in designing the ACC control strategy can significantly affect the dynamics characteristic of the simulated traffic flow, which can improve the traffic flow stability in the ITS environment.

Network Traffic Flow Evolution Model Based on Disequilibrium Theory

The disequilibrium theory in economics is used to depict the network traffic flow evolution process from disequilibrium to equilibrium. Three path choice behavior criteria are proposed, and the equilibrium traffic flow patterns formed by these three criteria are defined as price regulation user equilibrium, quantity regulation user equilibrium, and price-quantity regulation user equilibrium, respectively. Based on the principle of price-quantity regulation user equilibrium, the method of network tatonnement process is used to establish a network traffic flow evolution model. The unique solution of the evolution model is proved by using Picard’s existence and uniqueness theorem, and the stability condition of the unique solution is derived based on stability theorem of nonlinear system. Through numerical experiments, the evolution processes of network traffic flow under different regulation modes are analyzed. The results show that all the single price regulation, single quantity regulation, and price-quantity regulation can simulate the evolution process of network traffic flow. Price-quantity regulation is the combination of price regulation user equilibrium and quantity regulation user equilibrium, which thus can simulate the evolution process of network traffic flow with multiple user class.

Effects of vehicle gap changes on fuel economy and emission performance of the traffic flow in the ACC strategy.

This paper focuses on the effects of vehicle gap changes on fuel and emission performance of the simulated traffic flow in the adaptive cruise control (ACC) strategy. Firstly, the close correlation of vehicle gap changes and the host car's behaviors was explored with the measured car-following data. Secondly, the correlation between the host car's velocity and vehicle gap changes with different memory steps was also explored to develop the nth car’s optimal velocity function. Thirdly, a microscopic traffic simulation program was created for analyzing the traffic flow evolution process and approximately estimating the fuel consumptions and exhaust emissions. As a result, it was seen that vehicle gap changes with memory significantly affect fuel economy and emission performance of the simulated traffic flow in the ACC strategy, which can result in low fuel consumptions and exhaust emissions. This study is an incremental step forward for designing the control strategy of the ACC system.

Modeling and simulation of network traffic flow evolution based on incomplete information feedback strategies in the ATIS environment

Considering both the high complexity of urban traffic flow systems and the bounded rationality of travelers, providing traffic information to all travelers is an effective method to induce each individual to make a more rational route-choice decision. Within Advanced Traveler Information System (ATIS) working environment, temporal and spatial evolution processes of traffic flow in urban road networks are closely related to strategies of providing traffic information and contents of information. In view of the day-to-day route-choice situations, this study constructs original updating models of the cognitive travel time of travelers under four conditions, including not providing any route travel time, only providing the most rapid route travel time, only providing the most congested route travel time, and providing all the routes travel times. The disaggregate route-choice approach is adopted for simulation to reveal the relationship between the evolution process of network traffic flow and the strategy of providing traffic information. The simulation shows that providing traffic information to all travelers cannot improve the operational efficiency of road networks. It is noteworthy that an inappropriate information feedback strategy would lead to intense variation in various routes traffic flow. Compared with incomplete information feedback strategies, it is inefficient and superfluous to provide complete traffic information to all travelers.

An improved car-following model with multiple preceding cars’ velocity fluctuation feedback

In order to explore and evaluate the effects of velocity variation trend of multiple preceding cars used in the Cooperative Adaptive Cruise Control (CACC) strategy on the dynamic characteristic, fuel economy and emission of the corresponding traffic flow, we conduct a study as follows: firstly, with the real-time car-following (CF) data, the close relationship between multiple preceding cars’ velocity fluctuation feedback and the host car’s behaviors is explored, the evaluation results clearly show that multiple preceding cars’ velocity fluctuation with different time window-width are highly correlated to the host car’s acceleration/deceleration. Then, a microscopic traffic flow model is proposed to evaluate the effects of multiple preceding cars’ velocity fluctuation feedback in the CACC strategy on the traffic flow evolution process. Finally, numerical simulations on fuel economy and exhaust emission of the traffic flow are also implemented by utilizing VT-micro model. Simulation results prove that considering multiple preceding cars’ velocity fluctuation feedback in the control strategy of the CACC system can improve roadway traffic mobility, fuel economy and exhaust emission performance.

Modelling travellers’ en-route path switching in a day-to-day dynamical system

ABSTRACTTravellers’ en-route path switching is a very common travel adjustment behaviour which can significantly influence the whole day-to-day network traffic flow evolution process. This study encapsulated travellers’ sequential path adjustment mechanism into a day-to-day dynamical system, to capture travellers’ en-route switching effect without actually building a complicated within-day model to go with. According to different path choice behaviours and traffic information sources, three traveller groups were contained in the dynamical system, including the conservative travellers, the adventurous travellers unequipped with advanced traveller information systems (ATISs) and the ATIS-assisted adventurous travellers. In the proposed day-to-day dynamical model, a fixed point problem was established for achieving the heterogeneous traffic flow caused by travellers’ en-route path switching. Some stability analysis of the proposed dynamical system was accomplished in the numerical experiment. The effect of en-route path switching behaviour was investigated and it was found to influence both the stability of the dynamical system and the average travel time of adventurous travellers.

A Novel Method for Estimation of Dynamic OD Flow

To more accurately describe the evolution process of traffic flow, a novel method was proposed on the basis of the polynomial trend model and the Kalman filtering theory in the paper. The state variables were defined as the deviations of the actual OD flow from the historical values. These deviations were presented as a stochastic evolution process with a sliding trend. Furthermore, the dynamic OD matrix was estimated and predicated by establishing a polynomial trend filtering model. A large number of simulation results prove that the performance of the algorithm proposed in this paper is better than the traditional method, and this algorithm can acquire more accurate estimation and prediction information for OD matrix.

Sensitivity analysis based approximation models for day-to-day link flow evolution process

Compared with path-based day-to-day (DTD) traffic evolution models, link-based DTD traffic evolution models are easier to calibrate and validate. However, the inherent network loading sub-problem in link-based DTD models induces high computational burden which precludes their broad practical applicability. To address this challenge, this study proposes three approximation models for the DTD traffic flow evolution process based on the sensitivity analysis of the network loading sub-problem in a link-based DTD model. In particular, a first-order approximation (FOA) model is formulated based on the derivative of link flow solutions with respect to perturbations on network characteristics. To improve the approximation accuracy of the FOA model, a second-order approximation (SOA) model and a variable reduced approximation (VRA) model are developed. The applicability conditions of the proposed approximation models are derived. A small numerical example demonstrates that the FOA model performs well when perturbations are small and the approximation accuracy reduces as the scale of perturbations increases. The SOA and VRA models can improve the approximation accuracy of the FOA model, at the cost of computing the second-order derivative and the reference link flow pattern, respectively.

An improved car-following model with two preceding cars' average speed

To better describe cooperative car-following behaviors under intelligent transportation circumstances and increase roadway traffic mobility, the data of three successive following cars at a signalized intersection of Jinan in China were obtained and employed to explore the linkage between two preceding cars' average speed and car-following behaviors. The results indicate that two preceding cars' average velocity has significant effects on the following car's motion. Then an improved car-following model considering two preceding cars' average velocity was proposed and calibrated based on full velocity difference model and some numerical simulations were carried out to study how two preceding cars' average speed affected the starting process and the traffic flow evolution process with an initial small disturbance, the results indicate that the improved car-following model can qualitatively describe the impacts of two preceding cars' average velocity on traffic flow and that taking two preceding cars' average velocity into account in designing the control strategy for the cooperative adaptive cruise control system can improve the stability of traffic flow, suppress the appearance of traffic jams and increase the capacity of signalized intersections.

Quasi-Dynamic Model for Evolution of Network Travel Time under Incident

To describe the interaction and evolution rule of network travel time and route choice probability, the paper proposes a quasi-dynamic model with the road section flow state and logit principle. The diverge-merge model and function between speed and density is used to compute section storage vehicles and travel time of non-incident section by analyzing traffic flow evolution process of incident section. The Kinematic wave theory is adopted to compute queue length and travel time of incident section. The results indicate that: before incident, traffic flow and route choice probability approaches an equilibrium with a long-time simulation; during the incident period, because of the interactions among queue length, route travel time and route choice probability, these three variables present concussed. With the incident clearance, route travel time decreases continuously; after queue dispersing, the route travel time and route choice probability approaches a new equilibrium within certain time.

NETWORK ANALYSIS OF THE EVOLUTION OF TRAFFIC FLOW WITH SPEED INFORMATION

In the cellular automata traffic flow model, the traffic state can be represented by the discrete speed value of vehicles, thus the traffic flow can be deemed as a discrete dynamical system. In the evolution process of traffic flow, complex networks are constructed by representing the traffic state as node and the evolution relationship in timescale as link. The emerging times of link is defined as its weight, then the node strength is equal to the emerging times of the corresponding traffic state. As a result, a weighted network is obtained. The dynamics of stop-and-go traffic are studied by investigating the statistical properties of the network. Simulation results show that scale-free behavior commonly exists in the evolution process of stop-and-go traffic. The degree distribution, node strength distribution and link weight distribution have the power law form. The node with high degree also has large strength. The structure of the network is not influenced by the randomization probability and density as long as the stop-and-go traffic is reproduced.

One-dimensional traffic cellular automaton model with consideration of the change of driving rules

Based on the WWH and SDNS cellular automata （CA） traffic model, an improved single lane traffic CA model with consideration of the change of driving rules is proposed. The model considers the drivers adopting different driving rules under mutative traffic condition, and introduces the rules of driving method change. Numerical simulations have been carried out. The results show the complicated evolution process of traffic flow. Different values of change probability have different effect on mixed traffic flow. With the increase of change probability, aggressive vehicles cause greater effect. In the evolution process, the change frequency can be controlled by the definition of the change probability and safety probability. The traffic flow is higher in the new model than in the NS and SDNS model. This proves that the stop status of the whole traffic flow has been improved.

Relationship between microscopic dynamics in traffic flow and complexity in networks

Complex networks are constructed in the evolution process of traffic flow, and the states of traffic flow are represented by nodes in the network. The traffic dynamics can then be studied by investigating the statistical properties of those networks. According to Kerner's three-phase theory, there are two different phases in congested traffic, synchronized flow and wide moving jam. In the framework of this theory, we study different properties of synchronized flow and moving jam in relation to complex network. Scale-free network is constructed in stop-and-go traffic, i.e., a sequence of moving jams [Chin. Phys. Lett. 10, 2711 (2005)]. In this work, the networks generated in synchronized flow are investigated in detail. Simulation results show that the degree distribution of the networks constructed in synchronized flow has two power law regions, so the distinction in topological structure can really reflect the different dynamics in traffic flow. Furthermore, the real traffic data are investigated by this method, and the results are consistent with the simulations.

Scaling laws of the network traffic flow

In this work, a type of the evolution network is constructed in the evolution process of traffic flow. We study the influence of the traffic dynamics on the structural properties of the evolution network, and measure the probability distributions and scaling properties of the network. The traffic dynamics is simulated by using the city traffic model [i.e., the modified ChSch model, see E. Brockfeld, R. Barlovic, A. Schadschneider, M. Schreckenberg, Phys. Rev. E 64 (2001) 056132]. The topological structure of the evolution network is strongly related to the traffic dynamics and various distributions of the connections can be found under different traffic conditions.