Using gap sequences to estimate gap acceptance functions

Traditional gap acceptance functions have been estimated based on the first gap observed. In this paper we show that the critical gap of drivers is decreasing on the average, as they are waiting for an acceptable gap. Our gap acceptance function is based on a probit model which assumes a normal distribution of gaps across gaps and drivers.     

Implementing the maximum likelihood methodology to measure a driver’s critical gap

Most of the capacity calculation procedures for two-way stop-controlled (TWSC) intersections are based on gap acceptance models. Critical gap is one of the major parameters for gap acceptance models. The accuracy of capacity estimation is mainly determined by the accuracy of the critical gap. This paper focuses on the implementation of the maximum likelihood technique to measure a driver’s critical gap using field data. A methodology to define gap events is proposed, so that the accepted gaps and maximum rejected gaps required by the maximum likelihood technique could be obtained. Specific issues regarding multi-lane situations and major street right turn movement are discussed. Special conditions observed during the research are addressed when the proposed method cannot be applied directly, such as the existence of a mid-block refuge area where minor street drivers can seek gaps in a two-stage process, pedestrian blockage, and downstream queue spill back. The proposed method was adopted in measuring critical gap under US conditions during a research project, described by Kyte et al. (1996). ©     

Design of an intersection decision support (IDS) interface to reduce crashes at rural stop-controlled intersections

Rural, stop-controlled intersections pose a crash risk to drivers, particularly elderly drivers. This paper outlines the design phase of an infrastructure-based intersection decision support (IDS) system to help drivers make safer gap acceptance decisions at rural intersections. A human factors-based design process was conducted to determine the type of information that should be presented to drivers. Information considered important for presentation to the driver included showing the presence of gaps, indicating the size of available gaps, and/or judging the safety of available gaps. This paper discusses the process used to determine the appropriate design specifications for initial testing of the IDS system interface.     

Novel Methods and the Maximum Likelihood Estimation Technique for Estimating Traffic Critical Gap

Most unsignalised intersection capacity calculation procedures are based on gap acceptance models. Accuracy of critical gap estimation affects accuracy of capacity and delay estimation. Several methods have been published to estimate drivers' sample mean critical gap, the Maximum Likelihood Estimation (MLE) technique regarded as the most accurate. This study assesses three novel methods; Average Central Gap (ACG) method, Strength Weighted Central Gap method (SWCG), and Mode Central Gap method (MCG), against MLE for their fidelity in rendering true sample mean critical gaps. A Monte Carlo event based simulation model was used to draw the maximum rejected gap and accepted gap for each of a sample of 300 drivers across 32 simulation runs. Simulation mean critical gap is varied between 3s and 8s, while offered gap rate is varied between 0.05veh/s and 0.55veh/s. This study affirms that MLE provides a close to perfect fit to simulation mean critical gaps across a broad range of conditions. The MCG method also provides an almost perfect fit and has superior computational simplicity and efficiency to the MLE. The SWCG method performs robustly under high flows; however, poorly under low to moderate flows. Further research is recommended using field traffic data, under a variety of minor stream and major stream flow conditions for a variety of minor stream movement types, to compare critical gap estimates using MLE against MCG. Should the MCG method prove as robust as MLE, serious consideration should be given to its adoption to estimate critical gap parameters in guidelines. Copyright © 2012 John Wiley & Sons, Ltd.     

Connectivity’s impact on mandatory lane-changing behaviour: Evidences from a driving simulator study

The connected environment provides driving aids to help drivers making efficient and safe driving decisions. The literature to date is devoid of conclusive evidences of the connected environment’s impact on drivers’ mandatory lane-changing (MLC) behaviour. As such, the objective of this study is to examine MLC behaviour through a driving simulator experiment using the CARRS-Q Advanced Driving Simulator. Participants with diverse background performed the experiment in randomised driving conditions: baseline (without the driving aids), connected environment with perfect communication, and connected environment with communication delay. Repeated measure ANOVA in the form of linear mixed model and Generalized Estimation Equation (GEE) are employed to analyse various driving performance indicators during MLC event. We find that drivers in the connected environment tend to wait longer, increase the initial speed, and maintain a larger spacing, compared to when they are driving in the baseline condition. In addition, drivers in the connected environment are likely to reject fewer number of gaps and select relatively bigger gap sizes. Furthermore, post-encroachment time (PET) in the connected environment is higher across different gap sizes, indicating that the connected environment makes MLC safer. The GEE model on gap acceptance suggests that the perfect communication and communication delay has positive and negative impact on the accepted gap size, respectively, and the GEE model on lane-change duration indicates that lane-change duration tends to increase in the connected environment.     

Augmented Reality Vehicle system: Left-turn maneuver study

Augmented Reality “AR” is a promising paradigm that can offer users with real-time, high-quality visualization of a wide variety of information. In AR, virtual objects are added to the real-world view in real time. The AR technology can offer a very realistic environment for enhancing drivers’ performance on the road and testing drivers’ ability to react to different road design and traffic operations scenarios. This can be achieved by adding virtual objects (people, vehicles, hazards, and other objects) to the normal view while driving an actual vehicle in a real environment. This paper explores a new Augmented Reality Vehicle “ARV” system and attempts to apply this new concept to a selected traffic engineering application namely the left-turn maneuver at two-way stop-controlled “TWSC” intersection. This TWSC intersection experiment, in addition to testing the feasibility of the application, tries to quantify the size of gaps accepted by different driver’s characteristics (age and gender). The ARV system can be installed in any vehicle where the driver can see the surrounding environment through a Head Mounted Display “HMD” and virtual objects are generated through a computer and added to the scene. These different environments are generated using a well defined set of scenarios. The results from this study supported the feasibility and validity of the proposed ARV system and they showed promise for this system to be used in the field-testing for the safety and operation aspects of transportation research. Results of the left-turn maneuver study revealed that participants accepted gaps in the range of 4.0-9.0 s. This finding implies that all gaps below 4 s are rejected and all gaps above 9 s are likely to be accepted. The mean value of the left-turn time was 4.67 s which is a little bit higher than reported values in the literature (4.0-4.3 s). Older drivers were found to select larger gaps to make left turns than younger drivers. The conservative driving attitude of older drivers indicates the potential presence of reduced driving ability of elderly. Drivers’ characteristics (age and gender) did not significantly affect the left-turn time. Based on the survey questions that were handed to participants, most participants indicated good level of comfort with none or small level of risk while driving the vehicle with the ARV system. None of the participants felt any kind of motion sickness and the participants’ answers indicated a good visibility and realism of the scene with overall good system fidelity.     

Statistical estimation of the parameters of Daganzo's gap acceptance model

In a recent article in Transportation Research, Daganzo (1981) described a model of gap acceptance that permits the mean of the gap acceptance function to vary among drivers and permits the duration of the shortest acceptable gap for each driver to vary among gaps. The model contains several constant parameters whose values must be estimated statistically from observations of drivers' behavior. The results of numerical experiments reported by Daganzo (1981) suggested that the values of the parameters cannot be estimated by the method of maximum likelihood, which is the most obvious estimation technique, and Daganzo proposed using a sequential estimation method instead. The sequential method appeared to yield reasonable numerical results. In this paper, it is shown that subject to certain reasonable assumptions concerning the true parameter values and the probability distribution of gap durations, the maximum likelihood method does, in fact, yield consistent estimates of the parameters of Daganzo's model, whereas the sequential method does not. Hence, maximum likelihood is the better estimation method for this model.     

Delay to major street through vehicles at two-way stop-controlled intersections

This paper describes a methodology for predicting the delay to major street through vehicles at two-way stop-controlled intersections. This delay is incurred when major street left-turn demand exceeds the available storage area and blocks the adjacent through lane. The through lane blockage problem does not generally occur with significant frequency on streets with divided cross sections that have left-turn bays or lanes; however, it frequently occurs on undivided streets due to their lack of left-turn storage. To minimize this delay, through drivers often merge with vehicles in the adjacent through lane—if there is an adequate gap for them to safely merge into. If there is no merge opportunity, then the through drivers will stay in the inside lane until the queue ahead dissipates. The through vehicle delay predicted by the methodology was found to be relatively small (i.e. less than 5 s veh⁻¹) when compared with delays commonly incurred by non-priority movements at unsignalized intersections. However, when expressed in terms of total vehicle hours of delay, the effect can be quite significant. In general, through vehicle delay increases with increasing approach flow rate and left-turn percentage. However, at flow rates in excess of about 1400 veh h⁻¹, delays increase very rapidly and there is evidence that larger left-turn percentages may have lower delays. ©     

Personalised feedback and eco-driving: An explorative study

Conventional road transport has negative impact on the environment. Stimulating eco-driving through feedback to the driver about his/her energy conservation performance has the potential to reduce CO₂ emissions and promote fuel cost savings. Not all drivers respond well to the same type of feedback. Research has shown that different drivers are attracted to different types of information and feedback. The goal of this paper is to explore which different driver segments with specific psychographic characteristics can be distinguished, how these characteristics can be used in the development of an ecodriving support system and whether tailoring eco-driving feedback technology to these different driver segments will lead to increased acceptance and thus effectiveness of the eco feedback technology. The driver segments are based on the value orientation theory and learning orientation theory. Different possibilities for feedback were tested in an exploratory study in a driving simulator. An explorative study was selected since the choice of the display (how and when the information is presented) may have a strong impact on the results. This makes testing of the selected driver segments very difficult. The results of the study nevertheless suggest that adapting the display to a driver segment showed an increase in acceptance in certain cases. The results showed small differences for ratings on acceptation, ease of use, favouritism and a lower general rating between matched (e.g., learning display with learning oriented drivers) and mismatched displays (e.g., learning display with performance oriented drivers). Using a display that gives historical feedback and incorporates learning elements suggested a non-verifiable increase in acceptance for learning oriented drivers. However historical feedback and learning elements may be less effective for performance oriented drivers, who may need comparative feedback and game elements to improve energy conserving driving behaviour.     

Estimation of gap acceptance parameters within and across the population from direct roadside observation

This paper explores the feasibility of maximum likelihood as an approach to determine the parameters of gap acceptance functions when these functions vary from individual to individual. Specifically, it is shown that it is theoretically possible to estimate the average critical gap of a population of drivers (or pedestrians) and its variance, within and across individuals, from direct roadside observations. Although the Multinomial Probit Model provides a natural theoretical framework for the estimation of these parameters, the model seems not to be statistically estimable for this particular problem. It was shown, however, that if one of the parameters is known, the other two become estimable and a two-stage estimation process that takes into account this phenomenon can be utilized. The technique is demonstrated with the 203-driver data set included in Appendix A. The Multinomial Probit Model can also be used to determine simultaneously the mean critical gap, the mean critical lag (the first gap considered by a driver), and the variances of these. For the data set in Appendix A, the mean critical gap was significantly smaller than the mean critical lag, as one might expect. The techniques proposed in this paper have the further advantage of being statistically efficient with large data sets and of not requiring a panel of individuals to be observed under controlled conditions.     

Extensions of theoretical capacity models to account for special conditions

The computational procedures used to analyze two-way stop-controlled intersections were extended in the National Cooperative Highway Research Project 3-46 to account for a number of effects commonly observed at actual unsignalized intersections. This paper presents theoretical extensions that can account for commonly observed phenomena, such as two-stage gap acceptance when median storage is available; right-turn “sneakers” at flared minor-street approaches; non-random arrivals caused by upstream signals; impedance due to pedestrian crossings; and delay to major-street through vehicles using shared left-turn and through lanes. The individual effects are then combined into an analytical framework suitable for inclusion in the Unsignalized Intersections procedures of the 1997 “Highway Capacity Manual”. ©     

Design policies for sight distance at stop-controlled intersections based on gap acceptance

The current AASHTO policy for sight distance at stop-controlled intersections is based on a model of the acceleration performance of a minor-road vehicle turning left or right onto a major road and the deceleration performance of the following major-road vehicle. This paper develops and quantifies an alternative intersection sight distance model based on gap acceptance. The paper describes field studies that were performed to determine the critical gaps appropriate for use in sight distance design. It is recommended that the sight distance along the major road for a passenger car at a stop-controlled intersection be based on a distance equal to 7.5 s of travel time at the design speed of the major road. Longer sight distances are recommended for minor-road approaches that have sufficient truck volumes to warrant consideration of a truck as the design vehicle. ©     

Limited priority merge at unsignalized intersections

The development of a new gap acceptance model based on limited priority for the major stream is discussed. Field observations were carried out to identify the mechanism of the merging process taking place at unsignalized intersections under congested conditions. It was found that the major stream headways were increased due to the merging vehicles, particularly at high flows. A limited priority system is proposed based on the assumption that the major stream vehicles would be slightly delayed to accommodate the minor stream vehicles. Equations for capacity in the limited priority system are presented assuming the major stream vehicles to have a bunched exponential headway distribution and the minor stream drivers to be both consistent and homogeneous. The gap acceptance model based on the limited priority was then applied to the performance of roundabouts. It was found that the limited priority merge can have a significant effect on the entry capacity at two-lane roundabouts. A near linear relationship between the entry capacity and the circulating stream flow at two-lane roundabouts was identified which was similar to the empirical results from the UK. ©     

Integrated driving behavior modeling

This paper develops, implements and tests a framework for driving behavior modeling that integrates the various decisions, such as acceleration, lane changing and gap acceptance. Furthermore, the proposed framework is based on the concepts of short-term goal and short-term plan. Drivers are assumed to conceive and perform short-term plans in order to accomplish short-term goals. This behavioral framework supports a more realistic representation of the driving task, since it captures drivers’ planning capabilities and allows decisions to be based on anticipated future conditions.An integrated driving behavior model, which utilizes these concepts, is developed. The model captures both lane changing and acceleration behaviors. The driver’s short-term goal is defined by the target lane. Drivers who wish to change lanes but cannot change lanes immediately, select a short-term plan to perform the desired lane change. Short-term plans are defined by the various gaps in traffic in the target lane. Drivers adapt their acceleration behavior to facilitate the lane change using the target gap. Hence, inter-dependencies between lane changing and acceleration behaviors are captured.     

A lane-change trajectory model from drivers’ vision view

Car-following and Lane-changing are two fundamental tasks during driving. While many car-following models can be applied, relatively, only a few lane-changing models have been developed. Classical lane-changing models mainly focus on drivers’ lane selection and gap acceptance behaviors, but very limited research has paid attention to formulating detailed lane-changing trajectories. This research aims to fill the gap by proposing a lane-changing trajectory model, which is built directly from drivers’ vision view, to model detailed lane-changing trajectories. A large amount of data of reference angles, defined as the angle changes between the drivers’ vision angle and left or right lane line, were first extracted from the videos recorded by the vehicle traveling data recorders (VTDRs) installed in 11 taxies. A comprehensive data analysis indicates that same drivers show similarity of their daily lane-changing habit but with variety, and different drivers’ lane-change trajectory data show different lane-change “personality” including aggressive or non-aggressive behaviors. Based on these findings, this paper then proposed a hyperbolic tangent lane-change trajectory model to describe drivers’ detailed lane-change trajectories. The model is verified using both real data and simulation. The results show the proposed lane-change trajectory model can successfully describe drivers’ lane-changing trajectories. More importantly, some parameters in the model are directly associated to drivers’ driving characteristics during lane-change. With this unique feature, the proposed model can generate driver-specific lane-change trajectories. Such improvement could contribute to the future development of Advanced Driver Assistance Systems (ADAS).     

Pedestrian gap acceptance for mid-block street crossing

Abstract

This paper investigates pedestrians' traffic gap acceptance for mid-block street crossing in urban areas. A field survey was carried out at an uncontrolled mid-block location in Athens, Greece. Pedestrians' decisions and traffic conditions were videotaped in terms of the size of traffic gaps rejected or accepted, waiting times and crossing attempts and vehicle speeds. A lognormal regression model was developed to examine pedestrian gap acceptance. It was found that gap acceptance was better explained by the distance from the incoming vehicle, rather than its speed. Other significant effects included illegal parking, presence of other pedestrians and incoming vehicles’ size. A binary logistic regression model was developed to examine the effect of traffic gaps and other parameters on pedestrians' decisions to cross the street or not. The results reveal that this decision is affected by the distance from the incoming vehicles and the waiting times of pedestrians.     

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.     

Modeling car-following behavior on urban expressways in Shanghai: A naturalistic driving study

Although car-following behavior is the core component of microscopic traffic simulation, intelligent transportation systems, and advanced driver assistance systems, the adequacy of the existing car-following models for Chinese drivers has not been investigated with real-world data yet. To address this gap, five representative car-following models were calibrated and evaluated for Shanghai drivers, using 2100 urban-expressway car-following periods extracted from the 161,055 km of driving data collected in the Shanghai Naturalistic Driving Study (SH-NDS). The models were calibrated for each of the 42 subject drivers, and their capabilities of predicting the drivers’ car-following behavior were evaluated.The results show that the intelligent driver model (IDM) has good transferability to model traffic situations not presented in calibration, and it performs best among the evaluated models. Compared to the Wiedemann 99 model used by VISSIM®, the IDM is easier to calibrate and demonstrates a better and more stable performance. These advantages justify its suitability for microscopic traffic simulation tools in Shanghai and likely in other regions of China. Additionally, considerable behavioral differences among different drivers were found, which demonstrates a need for archetypes of a variety of drivers to build a traffic mix in simulation. By comparing calibrated and observed values of the IDM parameters, this study found that (1) interpretable calibrated model parameters are linked with corresponding observable parameters in real world, but they are not necessarily numerically equivalent; and (2) parameters that can be measured in reality also need to be calibrated if better trajectory reproducing capability are to be achieved.     

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.     

Optimal operation of displaced left-turn intersections: A lane-based approach

Displaced left-turn (DLT) intersections that resolve the conflict between left-turn and opposing-through movements at the pre-signal are probably the most extensively used innovative intersection designs. The DLT intersection concept can be extended to ten different types according to the location of the left-turn transition area, the number of DLT approaches, and the possible setting of the bypass right-turn lane. This paper presents a generalized lane-based optimization model for the integrated design of DLT intersection types, lane markings, the length of the displaced left-turn lane, and the signal timings. The optimization is formulated as a mixed-integer non-linear program. This program is further transformed to a series of mixed-integer linear programming problems that can be solved by the standard branch-and-bound technique. Results from extensive numerical analyses reveal the effectiveness of the proposed method, as well as the promising property of assisting transportation professionals in the proper selection of DLT intersection types, and the design of geometric layout and signal timings.