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). ©     

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. ©     

Modeling Capacity Reliability of Minor Roads at At-Grade Un-Signalized Intersections for Potential Performance Evaluation

Abstract

Given stochastic features of the demands on both the major road and the minor road at an at-grade un-signalized intersection, the capacity of the minor road is viewed as the vulnerable and critical part impacting on the overall capacity of the intersection. To facilitate the analysis of intersection performance reliability, the capacity reliability of the minor road is defined as the probability that the capacity of the minor road can accommodate a certain traffic demand at a certain degree of saturation. The headway distribution of traffic stream on major road is reflected by three types of distributions, namely, exponential distribution, shifted exponential distribution, and Cowan's M3 distribution. Based on field observations, the volumes on both major roads and minor roads are treated as correlated normal random variables. This paper presents the methods for modeling capacity reliability of the minor road at an at-grade un-signalized priority intersection. A method based on first-order reliability method is used to model the capacity reliability index. As important associated factors of capacity reliability analysis, the methods for modeling and analyzing capacity sensitivity of the minor road and reserve capacity of the priority intersection are also presented. A procedure for evaluating the intersection potential performance using capacity reliability, sensitivity and reserve capacity is developed and demonstrated with a numerical example. Finally, some new findings from the case studies are summarized.     

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.     

Extreme value methods for estimating road traffic capacity

Common sense suggests that, at any point on a road network, there is an absolute limit to the volume of traffic which can be carried. But previous attempts to measure this “limiting capacity” have met with difficulties. First, there may not be enough vehicles to saturate the section of road under observation. Second, the flow may be constrained by a bottleneck upstream or downstream. Third, even under favourable conditions, the flows actually observed at saturation point tend to vary over a wide range, giving little clear indication as to what the value of the limiting capacity might be. In this paper, consideration is given to the variations in flow which occur over a time during normal traffic conditions, and to the characteristics of the extreme values which occur from time to time under these conditions. Two distinct types of statistical theory can be applied to extreme values. First, one can apply straight- forward probability theory, to predict the largest flows likely to be observed during a given period, assuming an idealised traffic stream with a known flow counting distribution. Second, one can attempt to deduce an upper limit from observed flow data using asymptotic methods of the kind which are frequently used in connection with meteorological and flood defense problems. Both methods are applied to a sample of 9000 flow values recorded at a site in London. Both methods are shown to fit the data reasonably well, but only the asymptotic method reveals a clear upper limit. Possible applications of the method are briefly discussed.     

Evaluation of a transportation system employing autonomous vehicles

The problem of studying public transportation systems with autonomous vehicles is challenging because of behavioral differences that make existing models poorly fit and the technical difficulties involved in studying large autonomous systems operating on a grand scale. In this paper, we propose the following: (i) an autonomous transportation network setting; (ii) a method for modeling autonomous vehicles in simulation; and (iii) a high‐performance simulation platform that allows analysis and visualization of transportation technologies. Results from microsimulation confirm theoretical benefits and improvements from employing autonomous systems in an example setting and highlight the platform's general ability to allow researchers to implement novel transportation systems and study the cost benefit variations occurring between them. Copyright © 2017 John Wiley & Sons, Ltd.     

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.     

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.     

Vehicle actuated signal performance under general traffic at an isolated intersection

We study green extension of a two-phased vehicle actuated signal at an isolated intersection between two one-way streets. The green phase is extended by a preset time interval, referred to as critical gap, from the time of a vehicle actuation at an advance detector. The green phase switches if there is no arrival during the critical gap. We develop an exact model to study the intersection performance with traffic following Poisson processes. We further extend the model to approximate the case of general traffic. Our model in the general case works well compared with Monte Carlo simulation. A few major observations include: (1) The optimal critical gap decreases with the traffic; (2) The optimal critical gap can be much larger (up to 5 s) than the common presumption of 2–3 s; (3) Queue clearance policy is not nearly optimal in general even in the case of heavy traffic.     

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.     

A macroscopic theory for unsignalized intersections

The following paper presents a dynamic macroscopic model for unsignalized intersections which accounts for time-limited disruptions in the minor stream flow, even in free-flow conditions when the average flow demand is satisfied. It introduces a deterministic fictive traffic light to represent an average alternating sequence of available and busy time periods for insertion depending on the major stream flow. Two allocation schemes of the total outflow during green periods are developed to model the influence or non-influence of the minor stream over the major stream flow. The aggregation of the resulting dynamic flow variations gives relevant capacity values. Moreover, the model predicts accurate average vehicle delay and queue length estimates compared to theoretical and empirical data. It has three easy-to-measure parameters and can be integrated into a dynamic macroscopic simulation tool for urban networks.     

On the macroscopic stability of freeway traffic

A simple model of traffic flow is used to analyze the spatio-temporal distribution of flow and density on closed-loop homogeneous freeways with many ramps, which produce inflows and allow outflows. As we would expect, if the on-ramp demand is space-independent then this distribution tends toward uniformity in space if the freeway is either: (i) uncongested; or (ii) congested with queues on its on-ramps and enough inflow to cause the average freeway density to increase with time. In all other cases, however, including any recovery phase of a rush hour where the freeway’s average density declines, the distribution of flow and density quickly becomes uneven. This happens even under conditions of perfect symmetry, where the percentage of vehicles exiting at every off ramp is the same. The flow-density deviations from the average are shown to grow exponentially in time and propagate backwards in space with a fixed wave speed. A consequence of this type of instability is that, during recovery, gaps of uncongested traffic will quickly appear in the unevenly congested stream, reducing average flow. This extends the duration of recovery and invariably creates clockwise hysteresis loops on scatter-plots of average system flow vs. density during any rush hour that oversaturates the freeway. All these effects are quantified with formulas and verified with simulations. Some have been observed in real networks. In a more practical vein, it is also shown that the negative effects of instability diminish (i.e., freeway flows increase) if (a) some drivers choose to exit the freeway prematurely when it is too congested and/or (b) freeway access is regulated in a certain traffic-responsive way. These two findings could be used to improve the algorithms behind VMS displays for driver guidance (finding a), and on-ramp metering rates (finding b).     

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.     

A flexible traffic stream model and its three representations of traffic flow

To connect microscopic driving behaviors with the macro-correspondence (i.e., the fundamental diagram), this study proposes a flexible traffic stream model, which is derived from a novel car-following model under steady-state conditions. Its four driving behavior-related parameters, i.e., reaction time, calmness parameter, speed- and spacing-related sensitivities, have an apparent effect in shaping the fundamental diagram. Its boundary conditions and homogenous case are also analyzed in detail and compared with other two models (i.e., Longitudinal Control Model and Intelligent Driver Model). Especially, these model formulations and properties under Lagrangian coordinates provide a new perspective to revisit the traffic flow and complement with those under Eulerian coordinate. One calibration methodology that incorporates the monkey algorithm with dynamic adaptation is employed to calibrate this model, based on real-field data from a wide range of locations. Results show that this model exhibits the well flexibility to fit these traffic data and performs better than other nine models. Finally, a concrete example of transportation application is designed, in which the impact of three critical parameters on vehicle trajectories and shock waves with three representations (i.e., respectively defined in x-t, n-t and x-n coordinates) is tested, and macro- and micro-solutions on shock waves well agree with each other. In summary, this traffic stream model with the advantages of flexibility and efficiency has the good potential in level of service analysis and transportation planning.     

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. ©     

Educating parents to support children’s road safety: a review of the literature

ABSTRACT

This narrative review synthesised the limited work that has been carried out into road safety education targeting parents. Parent education appeared to have a positive impact on child safety seat use and children’s bike helmet use, but results regarding the impact of parent education on pedestrian safety were mixed. The review highlighted important gaps in the literature. A key gap being identifying effective ways to engage parents of low socioeconomic and ethnic minority backgrounds. Further, another gap is understanding effective ways to engage and support parents of children with additional needs to build their children’s road safety skills. There is some evidence that parent education has a positive impact on these “at-risk” groups, but little work on how to engage with these groups and the type of parent education required.     

Reducing bunching with bus-to-bus cooperation

Schedule-based or headway-based control schemes to reduce bus bunching are not resilient because they cannot prevent buses from losing ground to the buses they follow when disruptions increase the gaps separating them beyond a critical value. (Following buses are then overwhelmed with passengers and cannot process their work quick enough to catch up.) This critical gap problem can be avoided, however, if buses at the leading end of such gaps are given information to cooperate with the ones behind by slowing down.This paper builds on this idea. It proposes an adaptive control scheme that adjusts a bus cruising speed in real-time based on both, its front and rear spacings much as if successive bus pairs were connected by springs. The scheme is shown to yield regular headways with faster bus travel than existing control methods. Its simple and decentralized logic automatically compensates for traffic disruptions and inaccurate bus driver actions. Its hardware and data requirements are minimal.     

Multi-scenario optimization approach for assessing the impacts of advanced traffic information under realistic stochastic capacity distributions

In this study, to incorporate realistic discrete stochastic capacity distribution over a large number of sampling days or scenarios (say 30–100 days), we propose a multi-scenario based optimization model with different types of traveler knowledge in an advanced traveler information provision environment. The proposed method categorizes commuters into two classes: (1) those with access to perfect traffic information every day, and (2) those with knowledge of the expected traffic conditions (and related reliability measure) across a large number of different sampling days. Using a gap function framework or describing the mixed user equilibrium under different information availability over a long-term steady state, a nonlinear programming model is formulated to describe the route choice behavior of the perfect information (PI) and expected travel time (ETT) user classes under stochastic day-dependent travel time. Driven by a computationally efficient algorithm suitable for large-scale networks, the model was implemented in a standard optimization solver and an open-source simulation package and further applied to medium-scale networks to examine the effectiveness of dynamic traveler information under realistic stochastic capacity conditions.     

Developing Metro Systems in the People’s Republic of China: Policy and Gaps

Rapid urbanization has taken place in China since the Open Policy in 1978. In face of the growing demand for mobility in large cities, new metro systems were developed in large cities like Guangzhou and Shanghai. At present, there are seven cities with 10 metro lines under construction. What are the policy issues and major challenges of developing metro systems in China? This paper systematically reviews the current situation and highlights three major gaps that Chinese cities have to overcome in planning metro systems. They are the technology gap, the financing gap and the affordability gap. A discussion of these gaps in the Chinese context leads us to the conclusion that early planning and careful studies are important in the development of metro systems in China. Moreover, the existing official criteria (population and economic power) for approving the building of metro systems are insufficient and should be supplemented by more vigorous evaluation criteria.     

Estimation of population origin–interchange–destination flows on multimodal transit networks

Previous research has combined automated fare-collection (AFC) and automated vehicle-location (AVL) data to infer the times and locations of passenger origins, interchanges (transfers), and destinations on multimodal transit networks. The resultant origin–interchange–destination flows (and the origin–destination (OD) matrices that comprise those flows), however, represent only a sample of total ridership, as they contain only those journeys made using the AFC payment method that have been successfully recorded or inferred. This paper presents a method for scaling passenger-journey flows (i.e., linked-trip flows) using additional information from passenger counts at each station gate and bus farebox, thereby estimating the flows of non-AFC passengers and of AFC passengers whose journeys were not successfully inferred.The proposed method is applied to a hypothetical test network and to AFC and AVL data from London’s multimodal public transit network. Because London requires AFC transactions upon both entry and exit for rail trips, a rail-only OD matrix is extracted from the estimated multimodal linked-trip flows, and is compared to a rail OD matrix generated using the iterative proportional fitting method.