Modeling probability distribution of delay at signalized intersections

Accurate estimation of vehicle delay is difficult because of the randomness of traffic flow and large number of factors affecting intersection capacity. Existing delay models simplify the real traffic conditions and provide only approximate point estimates of average delay, whereas its variability should also be of interest. A stochastic model was used to study the changing probability distribution of delay. The model is based on sequential calculation of queue length probabilities with any type of arrival process. Delay probability distribution was investigated for different degrees of saturation, arrival types and control conditions. The variance of delay increases rapidly with degree of saturation and is inversely proportional to the approach capacity. Other parameters such as cycle time and saturation flow do not have a significant effect on delay distribution. Both the mean and variance of delay are sensitive to arrival process characteristics and increase with the variance of arrivals.     

Specification and calibration of a microscopic model for pedestrian dynamic simulation at signalized intersections: A hybrid approach

Macroscopic pedestrian models for bidirectional flow analysis encounter limitations in describing microscopic dynamics at crosswalks. Pedestrian behavior at crosswalks is typically characterized by the evasive effect with conflicting pedestrians and vehicles and the following effect with leading pedestrians. This study proposes a hybrid approach (i.e., route search and social force-based approach) for modeling of pedestrian movement at signalized crosswalks. The key influential factors, i.e., leading pedestrians, conflict with opposite pedestrians, collision avoidance with vehicles, and compromise with traffic lights, are considered. Aerial video data collected at one intersection in Beijing, China were recorded and extracted. A new calibration approach based on a genetic algorithm is proposed that enables optimization of the relative error of pedestrian trajectory in two dimensions, i.e., moving distance and angle. Model validation is conducted by comparison with the observed trajectories in five typical cases of pedestrian crossing with or without conflict between pedestrians and vehicles. The characteristics of pedestrian flow, speed, acceleration, pedestrian-vehicle conflict, and the lane formation phenomenon were compared with those from two competitive models, thus demonstrating the advantage of the proposed model.     

New approach for developing warrants of protected left-turn phase at signalized intersections

The research embodied in this paper presents a new approach for the development of guidelines for the installation of a protected left-turn phase at signalized intersections when permissive-only left-turn operation is present. This approach is based on maintaining intersection traffic operation at optimum efficiency. Three analyses were presented and discussed and they involved the use of the new approach on some hypothetical basic scenarios at a four-legged intersection with single lane in each approach. The first scenario involved exclusive left-turn lane operation while the other two scenarios involved shared-lane operation. Exhaustive signal optimization analyses were conducted using a signal optimization software package called “Signal Expert”. Regression models were developed from optimization results that allow the analyst to make the decision on protected left-turn phase installation using the basic input data of signal timing design without the need to perform field measurements. The regression results showed that the transition from permissive to protected/permissive left-turn operation, based on system optimization, is mainly a function of traffic conditions and that this transition (interface) is predictable. The results also suggested that these warrants are of reasonable accuracy when compared with those in the current practice.     

Optimization of pedestrian phase patterns at signalized intersections: a multi‐objective approach

This paper presents a multi‐objective optimization model and its solution algorithm for optimization of pedestrian phase patterns, including the exclusive pedestrian phase (EPP) and the conventional two‐way crossing (TWC) at an intersection. The proposed model will determine the optimal pedestrian phase pattern and the corresponding signal timings at an intersection to best accommodate both vehicular traffic and pedestrian movements. The proposed model is unique with respect to the following three critical features: (1) proposing an unbiased performance index for comparison of EPP and TWC by explicitly modeling the pedestrian delay under the control of TWC and EPP; (2) developing a multi‐objective model to maximize the utilization of the available green time by vehicular traffic and pedestrian under both EPP or TWC; and (3) designing a genetic algorithm based heuristic algorithm to solve the model. Case study and sensitivity analysis results have shown the promising property of the proposed model to assist traffic practitioners, researchers, and authorities in properly selecting pedestrian phase patterns at signalized intersections. Copyright © 2013 John Wiley & Sons, Ltd.     

Discharge headway at signalized intersections in Hong Kong

This paper reports the analysis and comparisons of discharge headways at 26 sites in Hong Kong. Previous studies here established good understanding of the average discharge headway under various conditions but very few studies dealt with discharge headway of individual vehicles which is a vital component in the traffic simulation at signalized intersections. This study that looked into the discharge headway of individual vehicles found that the discharge headway at different queue position follows the Type I Extreme Value Distribution. A method of estimating site‐specific parameters for this distribution has also been proposed.     

Maneuvers of motorcycles in queues at signalized intersections

The maneuvering models of motorcycles in previous studies often considered motorcycles' traveling in terms of movements in a physical static lane and not in terms of dynamic virtual lane‐based movements. For that reason, these models are not able to imitate motorcyclists' behavior well. This paper proposes a maneuverability model framework for motorcycles in queues at signalized intersections with considering the dynamic motorcycle's lane. The model includes (i) a dynamic motorcycle's lane to identify the current, left, and right lanes of the subject motorcycle, (ii) a threshold distance to determine when a motorcyclist starts to consider maneuvering, (iii) a lane selection model to identify the lane preferred by a motorcyclist, and (iv) a gap acceptance model to describe whether or not the lead and lag gaps are acceptable for maneuvering. The model framework captures the variation across the motorcyclist population and over time observations. The models were applied to Hanoi and Hochiminh city, Vietnam, based on microscopic data collected from video images. All of the parameters were estimated using the maximum likelihood method with the statistical estimation software GAUSS. The results show that 77.88% of the observed maneuvers – either staying in the current lane or turning left or right – could be modeled correctly by the proposed models. Copyright © 2010 John Wiley & Sons, Ltd.     

Pedestrian delay estimation at signalized intersections in developing cities

This paper proposes a pedestrian delay model suitable for signalized intersections in developing cities, on the basis of a field study conducted in Xi’an, China. The field study consisted of two parts: Part I involved only one crosswalk, and the signal cycle was divided into 13 subphases; Part II involved 13 crosswalks, but the signal cycles were only divided into green phases and non-green phases. It was found that pedestrian arrival rates were not uniform throughout cycles; pedestrians arriving during green phases might also receive delays; pedestrian signal non-compliance was so severe that delays were greatly reduced, but non-complying pedestrians might still receive delays; and for pedestrians walking different directions, though the relationships between average delay and arrival subphase were different, the overall average delays were almost the same. On the basis of the field study results, some assumptions are made about the relationship between average pedestrian delay and arrival subphase, and a new model is developed to estimate pedestrian delays at signalized intersections. The model is validated using the field data, and the validation results indicate that in Xi’an the new model provides much more accurate estimation than the existing models.     

Delay-based passenger car equivalents for trucks at signalized intersections

This paper presents a new methodology for computing passenger car equivalents at signalized intersections that is based on the delay concept. Unlike the commonly used headway-based methods that consider only the excess headway consumed by trucks, the delay-based approach fully considers the additional delay heavy vehicles cause on traffic stream. Delay-based passenger car equivalents are not constant, but depend on traffic volume, truck type and truck percentage. The field data indicated that the passenger car equivalents increase as the traffic volume and the percentage of heavy vehicles increase. The field data were used to calibrate TRAF-NETSIM simulation model that was used to cover a broad range of traffic conditions. Mathematical models to estimate the equivalencies were developed. The passenger car equivalent for single unit trucks vary from 1.00 to 1.37, and for combination trucks 1.00–2.18 depending on traffic volume and truck percentage. The passenger car equivalents are highly correlated with traffic volume and, to some degree, with percentage of heavy vehicles. Although the PCE of 1.5 recommended in the 1985 HCM seems to be more reasonable than the 2.0 recommended in the 1994 and 1997 HCM, both overestimate the impact of single unit trucks. For combination trucks, the 1997 HCM overestimates the capacity reduction effects of the trucks in most cases.     

A probabilistic approach to calculate capacity of signalized intersections with a red light camera

In recent years, red light cameras (RLCs) have been installed at many signalized intersections. The main reason behind installing RLCs is to reduce intersection‐related accidents caused because of a driver's behavior to cross the intersection when the signal turns red. By nature, if the driver is aware of the presence of RLC his or her driving behavior is bound to change. This behavioral change, however, may be intentional or unintentional. This may influence the utilization of yellow intervals resulting in a possible increase in dilemma zone, which in turn, may reduce the service capacity of the intersection. To accurately capture this capacity reduction, we present a probabilistic approach to modify the saturation flow rate formula in the Highway Capacity Manual that is currently used to calculate the capacity of signalized intersections. We introduce a new factor in the saturation flow rate calculation called red light reduction factor, to account for the capacity reduction owing to RLCs. Using field data from Baltimore, Maryland, we establish a relationship for the red light reduction factor. We then show that capacity of RLC‐equipped intersections is generally lower than that without RLCs. Although the percentage reduction in capacity of a single intersection may not seem significant, the cumulative impact of such reduction in a heavily traveled road network may be quite significant, resulting in significant loss in travel time. In future works, the systemwide capacity reduction owing to the presence of RLCs can be studied in congested transportation networks. Copyright © 2012 John Wiley & Sons, Ltd.     

Modelling and analysis of traffic queue dynamics at signalized intersections

The dynamics of formation and dissipation of queues at isolated signalized intersections are investigated by analyzing the vehicle conservation equation along the street. Solution of the conservation equation is obtained by the method of characteristics for general initial and boundary conditions, and the effect of the control variables (cycle length, green and red intervals) and system parameters (arrival rates, capacity) on the length of the queue is examined. The theoretical results are obtained by examining the dynamics of the shock waves which are formed because of the intermitted service of traffic by the signal. These results include analytical criteria for the development of saturated or unsaturated situations, analytical expressions for the maximum queue length and limits on the control variables so that the queues remain bounded. The basic findings of this study can be employed for the solution of the traffic signal optimal control problem.     

A study on adjustment factors for U-turns in left-turn lanes at signalized intersections

U-turns are treated as left-turns in the current procedures for estimating saturation flow rates at signalized intersections. While U-turning vehicles are usually mixed with left-turning vehicles in inside or left-turn lanes and conflict with opposing through traffic as left-turning vehicles, the vehicle operating characteristics are different. The objective of this paper is to investigate the effects of U-turns on the traffic flow in left-turn lanes. Field data of 600 headways of left-turning passenger cars and 160 headways of U-turning passenger cars are recorded. The average headways of U-turning passenger cars are found to be significantly larger than those of left-turning passenger cars. The effects of U-turning vehicles depend upon the percent of U-turning vehicles in the left-turn lane, as well as the order of formation in the traffic stream. Adjustment factors for varying percents of U-turning vehicles in left-turn lanes are established.     

Signal control optimization for automated vehicles at isolated signalized intersections

Traffic signals at intersections are an integral component of the existing transportation system and can significantly contribute to vehicular delay along urban streets. The current emphasis on the development of automated (i.e., driverless and with the ability to communicate with the infrastructure) vehicles brings at the forefront several questions related to the functionality and optimization of signal control in order to take advantage of automated vehicle capabilities. The objective of this research is to develop a signal control algorithm that allows for vehicle paths and signal control to be jointly optimized based on advanced communication technology between approaching vehicles and signal controller. The algorithm assumes that vehicle trajectories can be fully optimized, i.e., vehicles will follow the optimized paths specified by the signal controller. An optimization algorithm was developed assuming a simple intersection with two single-lane through approaches. A rolling horizon scheme was developed to implement the algorithm and to continually process newly arriving vehicles. The algorithm was coded in MATLAB and results were compared against traditional actuated signal control for a variety of demand scenarios. It was concluded that the proposed signal control optimization algorithm could reduce the ATTD by 16.2–36.9% and increase throughput by 2.7–20.2%, depending on the demand scenario.     

Analysis of yellow-light running at signalized intersections using high-resolution traffic data

Many accidents occurring at signalized intersections are closely related to drivers’ decisions of running through intersections during yellow light, i.e., yellow-light running (YLR). Therefore it is important to understand the relationships between YLR and the factors which contribute to drivers’ decision of YLR. This requires collecting a large amount of YLR cases. However, existing data collection method, which mainly relies on video cameras, has difficulties to collect a large amount of YLR data. In this research, we propose a method to study drivers’ YLR behaviors using high-resolution event-based data from signal control systems. We used 8 months’ high-resolution data collected by two stop-bar detectors at a signalized intersection located in Minnesota and identified over 30,000 YLR cases. To identify the possible reasons for drivers’ decision of YLR, this research further categorized the YLR cases into four types: “in should-go zone”, “in should-stop zone”, “in dilemma zone”, and “in optional zone” according to the driver’s location when signal turns to yellow. Statistical analysis indicates that the mean values of approaching speed and acceleration rate are significantly different for different types of YLR. We also show that there were about 10% of YLR drivers who cannot run through intersection before traffic light turns to red. Furthermore, based on a strong correlation between hourly traffic volume and number of YLR events, this research developed a regression model that can be used to predict the number of YLR events based on hourly flow rate. This research also showed that snowing weather conditions cause more YLR events.     

A measurement to driving situation awareness in signalized intersections

Drivers get involved easily in Left-Turn Across Path with Opposite Direction Traffic (LTAP-OD) conflicts at signalized intersection with unprotected left-turn phasing. This study classified the left-turn drivers’ performance into four types: (1) the correct acceptance of safe lags/gaps, (2) the correct rejection of dangerous lags/gaps, (3) the false rejection of safe lags/gaps and (4) the false acceptance of dangerous lags/gaps. Based on the high mounted video camera data, the logistic regression model was used to obtain the critical gaps for estimating whether the lags/gaps were safe or not. The results show that the cognition behavior of the left-turn drivers should be improved while the gap/lag is drawn near the critical gap. Furthermore, the conservative drivers are more likely to reject the larger lags/gaps and yield the right-of-way to the opposing vehicles. Simultaneously the poor response execution may cause drivers to have difficulties during the turning performance when the lags/gaps are large enough. These results could be used as the basis for a discussion of the right time to support the drivers.     

Exploration of correlation between environmental factors and mobility at signalized intersections

Characterizing the relationship between environmental factors and mobility is critical for developing a sustainable traffic signal control system. In this study, the authors investigate the correlation of the environmental impacts of transport and mobility measurements at signalized intersections. A metamodeling-based method involving experimental design, simulations, and regression analysis was developed. The simulations, involving microscopic traffic modeling and emission estimation with an emerging emission estimator, provide the flexibility of generating cases with various intersection types, vehicle types, and other parameters such as driver behavior, fuel types, and meteorological factors. A multivariate multiple linear regression (MMLR) analysis was applied to determine the relationship between environmental and mobility measurements. Given the limitations of using the built-in emissions modules within current traffic simulation and signal optimization tools, the metamodeling-based approach presented in this paper makes a methodological contribution. The findings of this study set up the base for extensive application of simulation optimization to sustainable traffic operations and management. Moreover, the comparison of outputs from an advanced estimator with those from the current tool recommend improving the emissions module for more accurate analysis (e.g., benefit-cost analysis) in practical signal retiming projects.     

Comparative analysis of the safety effects of electric bikes at signalized intersections

The paper compares the risk-taking behavior of the riders of electric-bikes and bicycles and their effects on safety at signalized intersections. Data were collected at signalized intersections in the city of Kunming in China. Traffic conflicts techniques are used to estimate the safety effects of electric-bikes and bicycles, with the incidents observed divided into sixteen types. About 77.7% of conflicts were caused by the risky behavior of the automobiles drivers that in particular did not yield right-of-way to electric-bikes/bicycles, 13.4% by the risky behavior of e-bikers, and the rest by cyclists. Red-light running was the leading cause for the conflicts in which the electric-bikes were at-fault.     

Severity of pedestrian injuries due to traffic crashes at signalized intersections in Hong Kong: a Bayesian spatial logit model

The present study intended to (1) investigate the injury risk of pedestrian casualties involved in traffic crashes at signalized intersections in Hong Kong; (2) determine the effect of pedestrian volumes on the severity levels of pedestrian injuries; and (3) explore the role of spatial correlation in econometric crash‐severity models. The data from 1889 pedestrian‐related crashes at 318 signalized intersections between 2008 and 2012 were elaborately collected from the Traffic Accident Database System maintained by the Hong Kong Transport Department. To account for the cross‐intersection heterogeneity, a Bayesian hierarchical logit model with uncorrelated and spatially correlated random effects was developed. An intrinsic conditional autoregressive prior was specified for the spatial correlation term. Results revealed that (1) signalized intersections with greater pedestrian volumes generally exhibited a lower injury risk; (2) ignoring the spatial correlation potentially results in reduced model goodness‐of‐fit, an underestimation of variability and standard error of parameter estimates, as well as inconsistent, biased, and erroneous inference; (3) special attention should be paid to the following factors, which led to a significantly higher probability of pedestrians being killed or sustaining severe injury: pedestrian age greater than 65 years, casualties with head injuries, crashes that occurred on footpaths that were not obstructed/overcrowded, heedless or inattentive crossing, crashes on the two‐way carriageway, and those that occurred near tram or light‐rail transit stops. Copyright © 2017 John Wiley & Sons, Ltd.     

Operational analysis of the contraflow left-turn lane design at signalized intersections in China

The primary objective of the study was to evaluate the impacts of an unconventional left-turn treatment called contraflow left-turn lane (CLL) on the operational performance of left-turn movement at signalized intersections. An analytical model was developed for estimating the capacity of left-turn movement at signalized intersections with the CLL design. The capacity model was calibrated and validated using field data collected at six approaches at five signalized intersections in the city of Handan, China. The results of field data analyses showed that the use of CLL design improved the capacity of left-turn movements. However, the capacity gains with the CLL design were quite stochastic considering the randomness in the arrivals of left-turning vehicles. Analytical delay models were proposed for estimating the delay to left-turning vehicles at intersections with the CLL design. A procedure was also proposed for optimizing the location of the upstream median opening and the green interval of the pre-signal. Simulation analyses were conducted to compare the delay experienced by the left-turning and through vehicles at signalized intersections with the conventional left-turn lane, the CLL and another unconventional left-turn treatment entitled “tandem design”. The results showed that both CLL and tandem designs outperformed conventional left-turn lane design; and the CLL design generated less delay to both the left-turning and through vehicles as compared with the tandem design.