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In alignment with climate change, the European Union endeavors to accelerate the electrification progress of the public transit system. In particular, Copenhagen in Denmark and Oslo in Norway develop a blueprint to have 100% public transit electrification by 2030 and 2028, respectively. In this study, the lifecycle approach is applied to explore the role of electric buses in the electrification progress of the public transport system in different European countries. To better model the energy/fuel consumption, we integrate the theoretical model of human thermal comfortable temperature into our proposed framework. We take into account the effects of weather, the daily operation characteristics, and the energy mix of different European counties, and evaluate the lifecycle environmental and economic performance of electric buses. The result shows that the public transportation system with both hybrid and electric buses can be good compensation between financial and environmental needs instead of using electric buses to replace all the conventional buses. Moreover, the operational plan of the public transportation system mixed with electric and hybrid buses may be adjusted according to the seasonal temperature variation so as to maximize the environmental benefits. Considering the different economic and environmental scenarios of energy sources, some EU countries would be able to reduce or remove the incentives for electric buses.

Sustainable development of carsharing plays an important role in reducing the number of private cars and relieving urban parking pressure. Understanding the behavior of users, such as spatiotempora...

Day-to-day traffic assignment models provide a powerful tool to analyze the time evolution of traffic flow within transport networks. In day-to-day dynamics, most models assume that there are only private cars on traffic networks and travelers update their choices each day. However, there are mainly two traffic modes, i.e. cars and buses, and travelers may not change their mode choices frequently. In this paper, a period-to-period traffic assignment model is proposed to capture traffic dynamics under traffic restrictions by considering interactions among different modes and introducing a delay about travelers’ mode choice. The existence and uniqueness of the equilibrium are analyzed. The linear stability of the equilibrium is analyzed and the eigenvalue range of Jacobian matrix is estimated by using the Gershgorin circle theorem. Both theoretical analyses and numerical simulations indicated that compared to the system with no mode choice, mode choice behaviors could improve the stability of the equilibrium. Additionally, mode choice behaviors with delay might further increase the stability domain and dampen oscillations on the cost and the flows. This study explains the evolution patterns of transportation networks under traffic policy and provides guidance for network design and management.

It is foreseeable that connected vehicles (CVs) and regular vehicles (RVs) will be operated together on roads in the upcoming decades. The appearance of CVs provides us an opportunity to improve tr...

Lane changing is one of the basic driving behaviours, which may induce traffic oscillations and incidents. However, it is difficult to well model the lane-changing decision process due to the compl...

Due to the interactions among adjacent roads in urban road networks, traffic congestion gradually propagates to neigboring roads, resulting in regional congestion. To develop advanced regional traffic control strategies, it is necessary to clearly understand the characteristics of regional congestion evolution. To this end, this paper proposes a data-driven approach to mine the spatiotemporal associations of regional traffic congestion. By introducing both time and space attributes, the intra-transaction spatiotemporal Apriori (IntraT-ST-Apriori) algorithm is developed to address the static features of regional traffic congestion; while the inter-transaction spatiotemporal Apriori (InterT-ST-Apriori) algorithm is developed to capture the dynamic characteristics of regional traffic congestion. Case studies are carried out for the urban road network in Tianjin, China, based on empirical data. The results indicate that the Intra-ST-Apriori algorithm can excavate the underlying associations of regional traffic congestion. Furthermore, the congestion propagation trajectories can be clearly revealed based on the InterT-ST-Apriori algorithm. It is expected that the proposed approach can support the regional traffic management and control, significantly relieving traffic congestion.

In the upcoming decades, connected vehicles will join regular vehicles to appear on roads, and the characteristics of traffic flow will be changed accordingly. To model the heterogeneous traffic mixing regular and connected vehicles, a generic car-following framework is first proposed in this paper. A linear stability condition is theoretically derived, which indicates that the stability of the heterogeneous traffic is closely related to the penetration rate and the spatial distribution of connected vehicles. The generic car-following framework is applied by taking the Intelligent Driver Model as an example, and it is shown that connected vehicles can obviously enhance the stability of traffic flow and improve traffic efficiency in particular when traffic is in congestion. Moreover, a driver assistance strategy based on distributed feedback control is developed for connected vehicles, and the simulation results show that the proposed driver assistance strategy performs satisfactorily in stabilizing traffic as well as improving traffic efficiency.

The paper aimed to explore the relationship between risks and individuals’ driving states and then design an efficient method to help drivers avoid high risks. The relationship between risks and individuals’ driving states was deeply studied first. Microscopic driving states were categorized into different clusters, and it was found that the risks are distinct in different clusters and a specific driver might experience different risks in car-following process. Then, according to these findings, a risk warning strategy was designed to help drivers avoid high risks. The risk warning is active when the risk is higher than its threshold. The Helly models were used to mimic the drivers’ reaction to study the influence of the warning strategy. Simulation results showed that with the consideration of the risk warning, the spacing obviously increases, and the oscillations of velocity and acceleration are significantly shrunk, and risks in the driving process dampen down. Because drivers can perceive high risks during the driving process, and then appropriately change their car-following decisions to avoid high risks. These findings are helpful to improve driving behaviors and promote traffic safety.

In this paper, a data-driven two-lane traffic flow model based on cellular automata is proposed. Long Short-Term Memory (LSTM) and Support Vector Machine (SVM) are used to learn the characteristics of car following behavior and lane changing behavior, respectively, from real operation data of vehicles. Under optimal network parameters, the mean absolute errors of the LSTM network for training and testing data are only 0.001 and 0.006, respectively; while the prediction accuracy of the SVM classifier for both data reaches higher than 0.99. Moreover, forward rules and lane changing rules which are more consistent with actual situation are designed. The simulation results show that: (1) the new model can reflect the first-order phase transition from free flow to synchronized flow; (2) the frequency of unsuccessful lane changing is near zero in low-density traffic areas, but increases sharply in high-density regions; and (3) the lane changing duration and unsuccessful lane changing frequency display similar trends as traffic densities increase.

Advanced information is increasingly being used as an external intervention tool to positively influence system performance. In many traffic assignment problems, the proportion of travellers that reroute is assumed to be constant (static rerouting behavior), whereas the number of travellers that modify their routes will change dynamically with the cost difference (dynamic rerouting behavior). In this paper, dynamic rerouting behavior is considered in day-to-day traffic assignment models to capture travellers’ reactions to advanced information. The properties of a dynamic rerouting weight function are studied using survey data. Our goal is to better understand the dynamic evolution of network flow. In the model, the rerouting weight varies dynamically with the cost difference between travellers’ estimated and expected costs. The linear stability of the equilibrium is analyzed. Both theoretical analyses and numerical simulations indicated that dynamic rerouting behavior increases the stability domain and decreases the parameter sensitivity. Additionally, the dynamic evolution of the cost and flow near the stability boundary is studied. The results show that the dynamic rerouting behavior helps to improve the convergence speed and dampen the oscillations in the evolution process. This paper explains the influence of dynamic rerouting choice behavior on the evolution patterns of transportation networks and provides guidance for network design and management.

Limited driving range, long charging time and high charging costs affect the use of battery electric vehicles (BEVs) for intercity travels and often compel drivers to charge their vehicles more than once. This study proposes a multistage optimisation model to provide BEV drivers with a charging strategy for intercity travel. This model aims to jointly minimise travel time and charging cost and to determine the optimal amount of charged energy in each charging station located along the available routes. A dynamic programming method for solving this model is also designed. The feasibility and effectiveness of the proposed model and solution method are verified through the numerical example and simulations. The results indicate that the trade-offs between travel time and charging cost significantly influence the proposed solution, and the residual energy at the destination affects the availability of routes. The policy implications for the BEV-based intercity travels are discussed.

Electric carsharing is considered as one of the leading solutions to alleviate traffic problems and promote the sustainable development of cities. However, extensive planning method is used to determine the carsharing station and capacity in the case of mismatch between supply and demand, which is not conducive to bring social benefits into play and leads to the imbalance between investment and profit. The reason is that the strategic planning of the stations has not been well studied, especially when considering the maximum profit and profit stability simultaneously. In response, an electric carsharing station optimisation method that considers various factors is proposed. A bi-level optimisation model for electric carsharing station, which considers profit of company and convenience of user, is constructed based on the survival analysis. Then, a case study is conducted in Lanzhou, China to validate the model. Results show that the method proposed is conducive to promoting the sustainable profit of electric carsharing companies. Budget, survival distance and cover rate have significant impacts on the profit of companies. In addition, improving profit value and stability requires trade-off under budget constraints in electric carsharing system.

In this paper, a two-lane cellular automata traffic flow model based on regular hexagonal cells is proposed. The realistic lane changing maneuvers with the lateral movement process, the lane changing duration, and the unsuccessful lane changing are considered by the new model. The vehicle trajectories from NGSIM dataset are used to extract the realistic lane changing maneuvers and calibrate the lane changing angle. The numerical results showed that the flow in the intermediate density range of the new model is lower than that of the traditional model. While the lane changing frequency in the same density range of the new model is higher than that of the traditional model. The lane changing duration will increase as the density grows. And the unsuccessful lane changing rate grows to large values in high density range. As to the heterogeneous traffic flow, the lane changing frequency is obviously greater than that in homogeneous condition. The trucks are more likely to make unsuccessful lane changing. And the lane changing duration of trucks is longer than that of cars in free flow region, but this is not the case in congested flow.

Car-sharing has been emergent in many cities all over the world due to the environmental sustainability and the diverse service for users. However, the huge investment and the long payback period hinder the development of car-sharing. To this end, this study attempts to mine the value of car-sharing users in terms of empirical data, aiming to provide suggestions for companies to enhance user management. Based on the order data of a car-sharing company, several indicators are defined. On the basis, the users are divided into three categories, namely high-value users, low-value users and potential users. Furthermore, with the proposed indicators and the personal attributes, a prediction model is developed based on random forest method to predict the category of users in advance. The results show that with the observation period of 7 weeks, the long-term value type of a user can be predicted with accuracy of more than 80%.

Driving behavior is heterogeneous for various drivers due to the different influencing factors as reaction time, gender, driving years and so on. Some existing works tried to reproduce some of the complex characteristics of real traffic flow by taking into account the heterogeneous driving behavior, and the drivers are generally divided into two classes (including aggressive drivers and careful drivers) or three classes (including aggressive drivers, normal drivers and careful drivers). Nevertheless, the classification approaches have not been verified, and the rationality of the classifications has not been confirmed as well. In this study, the trajectory data of drivers is extracted from the NGSIM datasets. By combining the K-Means method and Silhouette measure index, the drivers are classified into four clusters (named as clusters A, B, C and D, respectively) in accordance with the acceleration and time headway. The two-dimensional approach is applied to analyze the characteristics of different clusters. Here, one dimension consists of “Cautious” and “Aggressive” behaviors in terms of velocity and acceleration, and the other dimension consists of “Sensitive” and “Insensitive” behaviors in terms of reaction time. Finally, the fuel consumption and emissions for different clusters are calculated by using the VT-Micro model. A surprising result indicates that overly “cautious” and “sensitive” behaviors may result in more fuel consumption and emissions. Therefore, it is necessary to find the balance between the driving characteristics.

Travel demand is indeed stochastic with day-to-day travel demand variability, because of the underlying characteristic of variability of travel activities. The stochastic travel demand can be described by different probability distribution patterns and has to be considered in transport network design, as it affects travelers' routing choice behavior against stochastic travel time and eventually the traffic flow pattern on the network. However, on the other hand, because of the inaccurate or inconsistent travel demand estimation procedures, the prediction of the travel demand distribution pattern and parameters is susceptible to a certain level of uncertainty. Therefore, both the travel demand day-to-day variability and the uncertainty in terms of estimating travel demand distribution pattern and parameters have to be incorporated in the transportation network design. This study develops an approach to model network design problem with uncertain demand variability. Specifically, it is assumed that ...

Bicycle movements are always associated with lateral drifts. However, the impacts of lateral drift behavior, as well as variable lateral clearance maintaining behavior due to the variation of drift intensity, on mixed bicycle flow are not clear. This paper establishes a new cellular automata model to study typical characteristics of mixed bicycle traffic induced by lateral drift and its accompanying behavior. Based on derived positive correlation between passing speed and drift speed through survey, the occurrence probability of lateral drift and the degree of maintained lateral clearance are both introduced in accordance with the variance of passing speed. Then, in whole density region, firm conformity between simulation results and actual survey data is reached, which has seldom been achieved in previous studies. It is further verified that speed distortions in intermediate and high density region induced by assumption of constant lateral clearance requirements can be revised by introducing its variability characteristics. In addition, two contrastive impacts of lateral drift behavior are observed. That is, it causes speed fluctuation in low density while alleviating the speed fluctuation in relatively high density. These results are expected to be helpful to improve the simulation performance of mixed bicycle flow as well as depict more realistic vehicle-bicycle conflicts and so on.

In this study, a region-based dynamic model is proposed to depict the traffic dynamics of an idealised grid-like unidirectional road network, and the impact of heterogeneity of the network on macroscopic traffic flow is investigated. The equilibrium solutions are obtained by solving the dynamic model, and the method of linear stability analysis is applied to test the stability of the solutions. Accordingly, the curves of macroscopic fundamental diagram (MFD) for various inhomogeneous networks are plotted and the effects of network heterogeneity on MFD are revealed. Two network heterogeneity parameters, road capacity and the attraction strength of a sub-region in the road network, are considered and the results show that both of them affect the shape of MFD significantly. Numerical simulations are performed and the result supports the theoretical analysis.

With the development of intelligent transport system, advanced information feedback strategies have been developed to reduce traffic congestion and enhance the capacity. However, previous strategies provide accurate information to travelers and our simulation results show that accurate information brings negative effects, especially in delay case. Because travelers prefer to the best condition route with accurate information, and delayed information cannot reflect current traffic condition but past. Then travelers make wrong routing decisions, causing the decrease of the capacity and the increase of oscillations and the system deviating from the equilibrium. To avoid the negative effect, bounded rationality is taken into account by introducing a boundedly rational threshold B R . When difference between two routes is less than the B R , routes have equal probability to be chosen. The bounded rationality is helpful to improve the efficiency in terms of capacity, oscillation and the gap deviating from the system equilibrium.

To alleviate the traffic congestion on urban expressway, Variable Message Signs (VMS) have been widely employed for diverting some traffic to arterial streets in large cities. The diversion rate is a key parameter to design, operation and evaluation of the VMS. Many works have been done to study the diversion rate by stated preference survey. However, no consistent conclusion has been obtained on the key factors influencing diversion behavior. Therefore, this paper pays attention to analyzing the drivers’ diversion from expressway behavior under different network and traffic conditions, and finding the key factors influencing diversion behavior by using stated preference survey. In the survey, graphical traffic information is provided as scenario simulation. Ordinal regression method is adopted to explore the key factors influencing diversion willingness. Binary logit model is used to explore the divert decision with given traffic information. It is shown that driving years, income, driving style, average trip length, and degree of trust in VMS are the significant factors to diversion willingness. Furthermore, the same VMS displaying state results in different diversion flow at different sites. Those findings are the foundation to optimize traffic information releasing strategy and improve the road network efficiency.

With increasingly fierce competition making price becomes important question relating to the cruise industry. Focusing primarily on three factors, customer arrival rate, ticketing remaining cycles and the remaining tickets, we further improve dynamic pricing method to the market in which we consider random factors and calculate by MATLAB to reflect the impact of three factors on pricing and revenue. It shows that the customer’s arrival rate and the price have the same monotonicity and the more the ticketing remaining cycles are, the lower the price is and the higher the revenue is, and so does the remaining tickets, which is accordance with the actual situation.

The increase of air travel puts tremendous burden on airline companies. A time saving boarding strategy is required to improve the utilization of airplane boarding time and explore flexible time management strategies. Firstly, an improved boarding strategy is introduced by assigning individual passengers to seats based on the number of luggage they carry. Passengers with the most luggage board onto the plane first. To test the behavior of boarding strategies under different conditions, a sophisticated simulation environment based on cellular automata model is designed. Simulation results indicate that the improved boarding strategy shows an excellent efficiency and robustness comparing with other strategies.

Both on-ramps and off-ramps are typical bottlenecks in urban traffic system, where traffic congestions often appear. The system with an on-ramp and an off-ramp is regarded as the typical scenario to study the effect of the relative location of on-ramp and off- ramp. The system can be classified into two types, the case with an upstream on-ramp and that with a downstream on-ramp. CTM (Cell Transmission Model) is used to model the system and calibrated by the data from the Beijing 3rd ring road. The results show traffic flow characteristics in the two systems are far different. Especially, for the system with a downstream on- ramp, main road has the priority in the merge area, and CTM cannot describe traffic characteristics. Thus, by considering the priority, Mainline Priority CTM (MP-CTM) is presented to describe the characteristics. The simulation results suggest that MP- CTM fits the empirical data from Beijing 3rd ring road.

With the rapid increase of the private cars, urban road congestion is getting worse. As known, when the downstream section is free flow, the congestion for every bottleneck section starts from the bottleneck cell, and then gradually propagates towards its upstream. Many studies about bottlenecks are based on the assumption that the downstream of each bottleneck is free flow. In this paper, we have investigated ramp systems with the congested downstream. Based on the cell transmission model, a tri-cell ramp system with two bottlenecks is used as an example to explore what the convergence state of the bottleneck section is under the congested downstream section. Three cases have been studied: free-flow downstream, middle-state downstream, and the most congested downstream, and the different convergence states. The results show that 1) if the downstream of the bottleneck is the most congested, the upstream bottleneck section converges to the most congested state no matter what the initial state is; 2) if the downstream is congested, the upstream section converges to congested states, and the degree of congestion in the upstream section increases with; 3) the larger the density in the congested downstream is, the more congested the final state of the ramp system is.

As a typical bottleneck connecting freeway and common road, a ramp is an important traffic congestion area. Various traffic phenomena near ramps can be described by the Cell Transmission Model (CTM). However, real traffic data shows that traffic flow characteristics are far different for the ramp system with different ramp distances. The authors analyze traffic characteristics of ramp system with both an on-ramp and an off-ramp in Beijing 3rd ring road firstly. Then, it is found that ramp distance between the on-ramp and the off-ramp has a great impact on the capacity, due to the conflict of traffic flow between on-ramp and off-ramp. Finally the traffic conflict is considered in the merge cell and Capacity Drop CTM (CD-CTM) is proposed to embody the conflict. The simulation results suggest that CD-CTM fits the empirical data from Beijing 3rd ring road.

Car-sharing is a new transportation mode with the rapid development of mobile Internet. It is necessary for the operation companies to keep the number of carsharing users and intelligent transportation can be realized by discovering the users before they loss and preventing the loss. In this paper, based on the massive order data of a car-sharing company in Beijing, the behavior of the users is analyzed before they become silent. In the light of Logistic Regression Model, the loss rate of users in next month is predicted based on the car-renting behavior in the former three months, and some suggestions are proposed to prevent the loss. The result shows that there is a significant difference in the behavior between the lost users and non-lost users. The accuracy of the prediction is 97.9%. The method proposed in the paper provides a theoretical basis for enterprises to deal with the early warning and recall of the lost users.

Since car-sharing demand plays an essential role on the management and service of car-sharing system, this paper attempts to analyze the temporal and spatial characteristics of the car-sharing demand, aiming to discover spatial and temporal patterns and association rules. Based on a clustering algorithm (i.e., DBSCAN), the spatiotemporal characteristics of car-sharing demand are studied. On the basis, the demand is divided into various clusters in space. Furthermore, the correlations between any two clusters are studied. The results show that car-sharing demand is high on Friday, Saturday and Sunday, and has strong correlation with time and space. It is expected the results can support the management of car-sharing system, and further promote the service level for passengers.

In intelligent transport system, some advanced information feedback strategies have been developed to reduce the oscillations and enhance the capacity on the road level. However, seldom strategies have considered the information delay and user equilibrium (UE) objective. Here, a derivative cost feedback strategy (DCFS) is proposed to reduce the influence of the delay, based on the UE principle. The simulation results show that in both no-delay and delay information cases, DCFS are the best and can make the system reaching the UE. Because DCFS can predict the trend of the travel cost.

Characteristics of mixed traffic on a road with a signalized crosswalk are investigated by cellular automaton modeling. The interaction mechanism between vehicles and pedestrians is taken into account. Also, the inordinate behavior of vehicles near the crosswalk, and various behaviors of three types of pedestrians (i.e., careful pedestrians, normal pedestrians, and riskers), are incorporated into the proposed model. By using numerical simulations, the case for pedestrian flow consisting of careful and normal pedestrians is investigated. Phase diagrams and spatiotemporal diagrams are presented to show different traffic states. The results show that there is a critical value that divides the vehicle flow into a free flow portion and a congested flow portion. Interestingly, there are two critical values for pedestrian flow for a large signal cycle value, whereas there is only one critical value when the signal cycle value is smaller than a critical value. Finally, the variation of violating frequency...

An alternative floor field (FF) model is proposed by incorporating the agitated behavior and elastic characteristics of pedestrians. The agitated behavior which is regarded as an important factor to pedestrian dynamics is depicted by introducing a parameter to revise the transition probability of pedestrians to move to the neighboring cells. To characterize elasticity of pedestrians, it is assumed that a cell can hold more than one pedestrians in crowd condition, while it can hold only one pedestrian in normal condition. In addition, a method to deal with conflicts is employed by considering the effects of agitated behavior and desired velocity. Numerical simulations are carried out to investigate pedestrian evacuation from a room. The results show, that as the value of agitated parameter increases, the evacuation time decreases to the minimum value and then increases gradually. Also, the faster-is-slower effect which is obtained by some other simulation models can be reproduced by the proposed model. Finally, the influence of exit width and the corresponding mechanism on evacuation process is investigated which is expected to be helpful to the exit design of public rooms.

In order to capture the characteristics of carsharing users, we applied a data-driven method to classify the users into typical clusters according to the contributions to the carsharing companies. The data used in this study are collected in the order information from the carsharing company in Beijing, China. The RFM model is employed to determine the influencing factors for clustering analysis. Accordingly, the most recent consumption, consumption frequency and spending are adopted to represent the user value. The users can thus be classified into three groups, named as potential users, high value users and the loss of users. It is expected that the results can improve the user management of the carsharing company.

The original BML model is extended by introducing extended sites, which can hold several vehicles at each time-step. Unexpectedly, the flow in the extended model sharply transits from free-flow to global jams, but the transition is not one-order in original BML model. And congestion in the extended model appears more easily. This can ascribe to the mixture of vehicles from different directions in one site, leading to the drop-off of the capacity of the site. Furthermore, the typical configuration of free flowing and global jams in the extended models is disorder, different from the regular structure in the original model.

To depict the mixed traffic flow consisting of motorized (m-) and non-motorized (nm-) vehicles, a new cellular automaton model is proposed by combining the NaSch model and the BCA model, and some rules are also introduced to depict the interaction between m-vehicles and nm-vehicles. By numerical simulations, the flux-density relations are investigated in detail. It can be found that the flux-density curves of m-vehicle flow can be classified into two types, corresponding to small and large density regions of nm-vehicles, respectively. In small density region of nm-vehicles, the maximum flux as well as the critical density decreases with the increase of nm-vehicle density. Similar characteristics can also be found in large density region of nm-vehicles. However, compared with the former case, the maximum flux is much lower, the phase transition from free flow to congested flow becomes continuous and thus the corresponding critical points are non-existent. The flux-density curves of nm-vehicle flow can also be classified into two types. And interestingly, the maximum flux and the corresponding density decrease first and keep constant later as the density of m-vehicle increases. Finally, the total transport capacity of the system is investigated. The results show that the maximum capacity can be reached at appropriate proportions for m-vehicles and nm-vehicles, which induces a controlling method to promote the capacity of mixed traffic flow.

In this paper, a new two-dimensional car-following model is proposed to depict the features of mixed traffic flow consisting of motorized vehicles ( m -vehicle) and non-motorized vehicles ( n m -vehicle), based on the two-dimensional optimal velocity (OV) model by Nakayama et al. [A. Nakayama, K. Hasebe, Y. Sugiyama, Phys. Rev. E 71 (2005) 036121]. In the proposed model, velocity difference terms are introduced, which are regarded as important factors for traffic behavior. Numerical simulations are carried out to investigate the interaction between left-turning n m -vehicle flow and straight-going m -vehicle flow at a typical unsignalized interaction. The results show that the straight-going m -vehicle flow just next to n m -lane is disturbed more seriously than others. In addition, a well-known phenomenon in reality is observed that groups of m -vehicles and n m -vehicles pass through the intersection alternately.

Crosswalk with push button is prevalent in lots of cities for the purpose of promoting the efficiency of the crosswalk, and thus the delays of both vehicles and pedestrians can be reduced. This strategy has been confirmed to be effective in several developed countries. However, it is a pity that application of push button is aborted in some cities in China. In this work, diverse behaviors of vehicles and pedestrians are analyzed and discussed. Then, a microscopic model is developed by incorporating the interaction between vehicles and pedestrians. Numerical simulations are performed to reveal the characteristics of traffic flow and the efficiency of the signal control strategy. Also, the impacts of risker proportion and button reaction time, as well as the impacts of various behaviors as mass behavior, the patience of pedestrian and push button habit are investigated. It is expected that the results will be helpful to the strategy design of a signalized crosswalk in such developing countries as China.

In this work, a cellular automaton model is presented to depict the traffic flow at such a crosswalk with push button. The characteristics of vehicle flow with various arriving rate of pedestrians are investigated. Flux curves and spatiotemporal diagrams are plotted to show different traffic states and the phase transition features. A parameter, named as button reaction time, is introduced to represent the green time for vehicle flow after the button is pushed by a pedestrian. The effect of button reaction time on saturated flux is investigated. The results show that there is a critical value of button reaction time. The saturated flux increases rapidly when button reaction time is smaller than the critical value, while it increases slowly otherwise. Furthermore, theoretical analysis is performed and the results coincide with the simulation ones.