Gap Acceptance Theory Research Articles

Capacity Estimation for On-Ramp Merging Section of Urban Expressway Based on Time Headway Loss

This paper proposes a model for estimating capacity of on-ramp merging section of urban expressway based on dynamics and gap acceptance theory, considering lane-changing processes and time headway loss. Survey data were collected from on-ramp merging sections of shanghai urban expressway system and showed that capacity drop of on-ramp merging section is caused by drivers’ lane-changing which may lead to unsteady speed of vehicles and so prolonged time headway compared to the minimum time headway corresponding to the maximum capacity. Three parameters (optimal time headway, time headway loss, and interference quantity of lane-changing) are given and a methodology by accumulating time headway loss due to lane-changing is developed to estimate the capacity drop. Results’ comparisons between real data and microsimulation of on-ramp merging sections and sensitivity analysis show that the proposed model can produce reliable and accurate results. This study also reveals that ramp flow and the difference between the optimal speed and the lane-changing speed of fleet have a great impact on capacity drop. This study is beneficial to evaluate congestion levels, to understand complex traffic phenomena, and so to find efficient solutions.

Capacity Prediction Model Based on Limited Priority Gap-Acceptance Theory at Multilane Roundabouts

Capacity is an important design parameter for roundabouts, and it is the premise of computing their delay and queue. Roundabout capacity has been studied for decades, and empirical regression model and gap-acceptance model are the two main methods to predict it. Based on gap-acceptance theory, by considering the effect of limited priority, especially the relationship between limited priority factor and critical gap, a modified model was built to predict the roundabout capacity. We then compare the results between Raff’s method and maximum likelihood estimation (MLE) method, and the MLE method was used to predict the critical gaps. Finally, the predicted capacities from different models were compared, with the observed capacity by field surveys, which verifies the performance of the proposed model.

Estimation of Critical Gap Based on Raff’s Definition

Critical gap is an important parameter used to calculate the capacity and delay of minor road in gap acceptance theory of unsignalized intersections. At an unsignalized intersection with two one-way traffic flows, it is assumed that two events are independent between vehicles' arrival of major stream and vehicles' arrival of minor stream. The headways of major stream follow M3 distribution. Based on Raff's definition of critical gap, two calculation models are derived, which are named M3 definition model and revised Raff's model. Both models use total rejected coefficient. Different calculation models are compared by simulation and new models are found to be valid. The conclusion reveals that M3 definition model is simple and valid. Revised Raff's model strictly obeys the definition of Raff's critical gap and its application field is more extensive than Raff's model. It can get a more accurate result than the former Raff's model. The M3 definition model and revised Raff's model can derive accordant result.

Capacity of U-turn Junction at Midblock Median Opening on Urban Arterial Based on Balancing Volume-to-capacity Ratio

U-turn at midblock median opening is frequently provided in developing countries to facilitate the local access. Movement capacity of such u-turns is of interest for deciding the necessary traffic management. HCM 2010 contains the methodology for u-turn capacity estimation, which is based on gap acceptance theory and assumption of major traffic headway distribution. This research evaluated the gap acceptance capacity model and proposed an adjustment method by v/c balancing. Data collection at a u-turn site was conducted for validation. The results showed that the gap acceptance capacity overestimated the field capacity in case of negative exponential headway distribution and underestimated in case of Erlang-2 headway distribution. The difference in driver behavior when responding to different conflicting headway could explain the situation. The proposed adjustment could provide the estimated capacity closer to the measured field capacity. The method also incorporated the interactions between the u-turn and through traffic streams.

Research on Conflict Point Delay of Left-turning Vehicles at Two Phases Signal Control Intersection

Analysis of intersection delay is important for intersection signal timing. Based on the gap acceptance theory, the conflict point delay of left-turning vehicles crossing opposing flow in mixed traffic at two phases signal control intersections is set up with probability theory. Observed values of conflict point delay of left-turning vehicles are compared with the calculated values from the model by choosing some certain intersections in Nanjing. Relationships among conflict point delay of left- turning vehicles, volume of opposing flow and composition of left-turning vehicles has been analyzed. The result shows that the model accords with the actual traffic flow condition at a two phases signal control intersection.

Variable Speed Limit Control on Highway Work Zone Considering Large Vehicle Mix Rates

Due to the difference of vehicle type and power performance between large vehicles and cars, large vehicle mix rate will have an important impact on traffic flow of work zone and lead to the decrease of driving safety. Through a survey of ShangHai outer ring highway work zone, this article analyzes the influence of large vehicles to traffic flow speed and speed variance, and then put forward a variable speed limit (VSL) strategy based on gap acceptance theory for highway work zone considering large vehicle mix rate. The simulated analyses showed that this strategy can reduce speed variance which can contribute to improving the overall traffic safety in work zone. The research results can provide a powerful technical support for highway work-zone speed management.

Key Variables of Merging Behaviour: Empirical Comparison between Two Sites and Assessment of Gap Acceptance Theory

This paper presents two empirical trajectory data sets focusing on the merging behaviour on a motorway, both in the Netherlands and in France. A careful review of the literature shows that the main theories explaining this behaviour rely on the hypothesis of gap acceptance, i.e. the fact that each driver has a certain threshold value depending on among other things the distance to the end of the acceleration lane, and when the offered gap is larger than this threshold the driver decides to merge.We conducted a detailed comparative analysis of the two data sets examining the main variables identified in our conceptual model of merging behaviour. The contribution of this paper is that the analysis does not only focus on the accepted gaps, but it also takes into account the rejected gaps. The comparison of our observations with the critical gap formula in literature showed that this formula does not take into account the strong probability of rejecting a gap, even larger than the gap finally accepted.Moreover, we created a logistic regression model that predicts the acceptance or rejection of a given gap, depending on the gap value and the speed difference between the merging vehicle and the putative follower. We have shown that two other factors impact the probability of rejecting or accepting a given gap, but these are significant for just one of the data sets: the distance to the end of the acceleration lane and the speed difference between the putative follower and the putative leader. This shows the impact of the local situation on the merging behaviour (e.g. traffic composition, road geometry, and traffic conditions).

Estimating the parameters of Cowan’s M3 headway distribution for roundabout capacity analyses

Capacity models based on the gap acceptance theory are widely used in unsignalised intersections and roundabout capacity analysis. These models are based on the statistical distribution of major vehicle headways. In this field, Cowan’s M3 distribution is usually recognized as the most adequate, but the estimation of its parameters is not trivial. In this paper, the main estimation methods are reviewed and a new method (Simultaneous Numerical Estimation – SNE) is proposed. The SNE method was used to develop a calibrated relation between parameters, using field data collected in Portuguese roads and roundabouts. It was determined that the new formula improves capacity estimates, either in one-lane or in two-lane roundabouts. The paper also addresses the importance of each input variable and parameter in the resulting capacity model, through a sensitivity analyses.

Minor Capacity Analysis of N Major Traffic Streams at Intersection

Based on the gap acceptance theory, this paper analyzed running state of the intersection streams about the main traffic priority controls. Theories were used in this paper, such as gap theory, the probability theory and the calculation methods of minor capacity under two vehicle streams. The calculating formula of minor capacity for n main vehicle streams was derived under the conditions of M3 distribution by the main stream headway at the uncontrolled intersection.

Microscopic dynamic simulation model for pedestrian at signalized intersection

Pedestrian’s road-crossing model is the key part of micro-simulation for mixed traffic at signalized intersection. To reproduce the crossing behavior of pedestrians, the microscopic behaviors of the pedestrians passing through the crosswalk at signalized intersection were analyzed. A pedestrian’s decision making model based on gap acceptance theory was proposed. Based on the field data at three typical intersections in Beijing, China, the critical gaps and lags of pedestrians were calibrated. In addition, considering pedestrian’s required space, a modification of the social force model that consists of a self-deceleration mechanism prevents a simulated pedestrian from continuously pushing over other pedestrians, making the simulation more realistic. After the simple change, the modified social force model is able to reproduce the fundamental diagram of pedestrian flows for densities less than 3.5 m−2 as reported in the literature.

Comparing Performances of Turbo-roundabouts and Double-lane Roundabouts

Starting from assumptions regarding the arrival process of circulating streams and according to models based on the gap-acceptance theory, the paper is aimed at comparing operational performances between basic turbo-roundabouts and double-lane roundabouts. The paper proposes applications of the Hagring model for entry capacity estimations at double-lane roundabouts and turbo-roundabouts, these latter, in particular, featured by movements with only one or two conflicting traffic streams. This model allows to use, in fact, a bunched exponential distribution to quantify the distribution of major vehicle headways; it also considers specific values different by each lane for behavioural parameters, minimum headway and conflicting traffic flow on circulating lanes. The results obtained for the two cases examined, although influenced by the underlying assumptions, especially with regard to user behaviour at turbo-roundabouts, can give information about the convenience in choosing, at a design level, a basic turbo-roundabout rather than a double-lane roundabout. The comparison developed in this paper, indeed, can be helpful in selecting the type of roundabout and in particular in evaluating performance benefits that are obtainable from the conversion of an existing double-lane roundabout to a turbo-roundabout with similar footprint of space.

Researching a Capacity Model for Multilane Roundabouts with Negotiation of the Right-of-Way between Antagonist Traffic Flows

This article summarizes a research program designed to assess operating conditions through capacity estimation at not-conventional roundabouts characterized by a central island with a large diameter and by two (or more) entering and circulating lanes. Although giving priority to vehicles on circulatory roadway is the nominal operating rule, on-field observations highlighted that in some infrastructural schemes of the type considered in this research drivers negotiate the right-of-way according to a consensus pattern that alternates between antagonist traffic flows, similarly to that observed at all-way-stop-controlled intersections. Considering the peculiarity of the way of working at roundabout schemes being examined, as well as difficulties faced in the application of models based on gap-acceptance theory to evaluate performances, an analytical capacity model derived from field observations was proposed for multilane not conventional roundabouts. Drawing inspiration from the iterative procedure proposed for capacity estimates at all-way-stop-controlled intersections, a calculation algorithm organized in 5 subsequent computational steps was developed in order to evaluate capacity at each entering/circulating lane for the type of roundabouts examined in this research. Results compared to those calculated by models for modern roundabouts show the effect on estimates of capacity raised by a more realistic operating pattern and indicate that the capacity model may be able to estimate parameters useful for planning and design purposes.

Study of Setting Conditions of Bus Bay Stop of Single Driveway

AbstractAimed at the capacity reduction factor of outside lane when buses move in and out of bus stops, using the related results of queuing theory and gap acceptance theory, the setting conditions of margin for the stops of single driveway were discussed. The influence time models of linear bus stops and bus bay stops of mobile driveway were established separately. Then, considered the delay of bus moving out of bus stop and service intensity as the constraint conditions, the capacity calculation model and condition setting model of mobile driveway were worked out. At last, the simulation experiment and model calculation results was comparative analysed, the adaptability check of models was performed, and the ranges of capacity with different bus arriving rates were given. The results show that the setting conditions of bus bay stops of single driveway are 518–1262 veh/h and 518–1243 veh/h separately when the arriving rates of buses are 20 veh/h and 30 veh/h. So the suggested models have high accurac...

Research on Capacity of Roundabouts in Beijing

Weaving section have b1een shown to have an effect on capacity at roundabout approaches, because at weaving sections conflict and interference increases, resulting in a reduction of speed. The weaving section is the bottleneck of the traffic flow. Therefore, it should be given the highest priority in the capacity analysis. The current method of calculating the approach capacity at a roundabout mainly utilizes information about entry and exiting vehicles. Few studies are currently conducted from view of the weaving section in capacity estimation. The purpose of this research is to estimate the capacity of roundabout by modeling weaving gap acceptance at the weaving sections. For this reason, a total of 21 roundabouts which are located at the downtown and the suburb of Beijing are selected to conduct data collection. Significance analysis of speed at weaving sections has been conducted by means of the variance analytic method. Regression models of the entry vehicles and circulating vehicles are built up. Based on gap acceptance theory a new method is proposed to estimate the capacity of roundabouts. Furthermore, the relationship between the left turn and through movements on the capacity of roundabouts is established. The findings from this research demonstrate that capacity estimates with weaving section vehicles result in improved prediction of the actual capacity of a roundabout. Furthermore, the geometrical design of roundabout is another important factor which influence the capacity of roundabout, needs to be further explored.

Quantifying the Number of Lane Changes in Traffic

Lane changes are an important aspect of freeway flow. Most models of lane change are microscopic. Lane change behavior of individual vehicles or drivers is described, and, therefore, models are calibrated microscopically. Macroscopic validation often is restricted to the distribution of vehicles across lanes. To the best of the authors' knowledge, no systematic analysis has been made of the number of lane changes as a function of the operational characteristics of the origin and target lane. This paper fills the gap in lane change literature with an analysis of the number of lane changes as a function of several incentives. On the basis of data availability, two “simple” sites were selected, that is, as close as possible to a straight continuous freeway. Statistical analysis at the selected sites revealed that drivers changed lanes on average once per 2 km driven. Furthermore, an analysis of the number of lane changes (per kilometer per hour) as a function of the density in the origin lane and in the target lane showed that the number of lane changes increased with the density in the origin lane for a fixed density in the target lane. The number of lane changes also increased with the density in the target lane for a fixed density in the origin lane. The underlying mechanism was therefore different from gap-acceptance theory. The analyses presented in this paper can be used to verify qualitatively (microscopic and macroscopic) lane change models and to propose better ones.

Research on Calculation Model of Minimum Net Distance between Interchanges on Eight-Lane Expressway

According to traffic operation characteristics and lane changing maneuvers, combining with the export notice signs and considering the worst driving conditions, the gap acceptance theory and kinematics are employed to establish the length of lane change operation between interchanges with probability theory. To operating speed as the premise, the necessary length that drivers change to the inside lane from the nearside lane is analyzed in terms of waiting for the gap acceptance, and the necessary length that drivers change to the nearside lane from the inside lane is also analyzed in terms of running for the gap acceptance, then calculation model of minimum net distance between interchanges on eight-lane expressway is constructed. The recommended value is then put forward.

Study on the Interference Ratio of Right-Turning Vehicles at Signalized Intersection under Mixed Traffic Environment

The objective is to describe the interference degree between motor vehicles and bicycles at signalized intersection. The interference degree was expressed by conflict delay. Via analyzing the microscopic actions of the motor vehicles crossing through the bicycle flow at a typical two-phase signalized intersection, a conflict delay model of the right-turn vehicle was proposed applying the gap acceptance theory and traffic wave theory. The model was verified and compared with the existing conflict delay models. The result showed that the proposed model is stable and suitable for the condition of unsaturated to calculate the conflict delay of right-turn vehicle. Sensitivity of the conflict delay model with respect to the flow rate of the bicycle and the width of the bicycle lane was analyzed. It showed that the increase of the width of the bicycle lane within limits could reduce right-turning vehicle’s conflict delay effectively when the motor vehicle’s flow rate was higher and the bicycle flow rate was varying in a certain range.

Development of Managed-Lane Access Guidelines Based on Gap Acceptance Theory

One strategy for improving freeway performance is implementation of managed lanes (MLs). Vehicles access an ML located in the freeway median by weaving across the general purpose lanes (GPLs) and entering the ML from the leftmost lane of the GPLs. Such intense lane-changing maneuvers cause traffic turbulence, which induces special operational problems with capacity, level of service, and safety. The principal objective of this research is to develop design guidelines for the ML access (or exit) spacing between the entrance (or exit) ramp and the ML access opening and for the ML access opening length. This research develops analytical weaving models based on gap acceptance theory; the models estimate the probability of successful weaves in these weaving distances. The research also develops design guidelines for these distances on the basis of the analytical weaving models.

Analysis and Modeling of Crossing Behavior at Urban Intersections in China

Crossing behaviors at intersections are conventionally described through the gap acceptance theory; however, many gap-forcing behaviors exist at Chinese urban intersections. In this study, gap-forcing behaviors were analyzed and modeled from the perspective of conflict avoidance using a new modeling methodology called virtual field graph. After providing the definition of the preemptive status and the method to calculate the preemptive level, a new driving behavior model that differentiates from the conventional gap acceptance model was established. Analysis of collected field conflict data indicates that 82.2% of drivers’ decisions are normal decisions, while 17.8% are abnormal decisions. This suggests that there should be a physiological critical preemptive level while the drivers are making decisions. The driving population’s critical preemptive level was calibrated with the collected field conflict data through the logistic regression method and maximum likelihood approach.

Modeling On-ramp Capacity with Driver Behavior Variation

Considering the variation of drivers' merging behaviors on the on-ramp of urban expressway, a gap acceptance theory model with variable critical gaps is proposed to measure the on-ramp capacity. When drivers travel along the acceleration lane of an on-ramp, the closer the driver is to the end of the acceleration lane, the stronger the driver's intention of merging into the main road would be, and a smaller critical gap will be selected. Consequently, the drivers' critical gap of merging decreases along with the acceleration lane of an on-ramp, which leads to the theoretical capacity of on-ramp at different position in the acceleration lane changed as well. Finally, a numerical example is given to illustrate the difference in capacity between the variable and fixed critical gap condition. The results indicate that the on-ramp capacity of the proposed model is always larger than those of the conventional model with fixed critical gap. Moreover, the above-mentioned difference is more obvious under oversaturation conditions.