Headway Distribution Research Articles

Fitting time headway and speed distributions for bicycles on separate bicycle lanes

Abstract The increasing sensitivity of policy-makers towards more sustainable and healthy transport is leading to increased interest in cycling, especially in urban areas. However, at the same time, recent studies in Europe, US and other countries have stressed the fact that cyclist fatalities are still alarmingly frequent, and lead researchers to want improved knowledge about bicycle traffic flow theory and modeling. The challenge is to make available robust analysis methods and models for building effective and safe infrastructures, for increased cycling mobility combined with positive effects on transport and social systems. This work presents the application of a procedure for fitting bicycle time headways and bicycle speed distributions from traffic data collected along bike tracks. The general frame of the procedure, together with functional components and their mutual interactions, are reported here. The effects of flow rate in both directions (analyzed and opposite) on time headway and vehicle speed distributions were examined. The possibility of associating the probability density functions of bicycle time headways and speeds in various cycling traffic conditions is a significant and interesting advance with respect to previous works. The procedure was applied to cross-sections belonging to the cycling network of the city of Bologna (Italy). The analysis compared a set of headway and speed distribution models, highlighting their goodness-of-fit with reference to empirical distributions.

Variability of Green Time to Discharge a Specified Number of Queued Vehicles at a Signalized Intersection

The aim of this paper is to study the headway distribution of queued vehicles (less than 16 vehicles) at signalized intersections. Existing studies usually take the average statistics of headway at any queuing place. When different percentile points of statistical data are assigned to headway, the passing rate (the rate of all queued vehicles passing the stop line) under the ideal signal timing scheme varies. When selecting the mean value, the passing rate of a queue of fewer than 16 vehicles is no more than 65%. When selecting 75% as the percentile, the passing rate is up to 94%. The queue length also decides the assigned percentile of headway to ensure the passing rate reaches a certain level. The value assignation of headway directly affects lane capacity and start-up loss time. This paper provides a new perspective on parameter calibration and will make the signal timing algorithm method more effective.

Understanding differences in emergency escape and experimental pedestrian crowd egress through quantitative comparison

Models of pedestrian crowd behavior in panic or emergency situations rarely have complementary empirical data to calibrate or validate the model's prediction. Till date, there is no systematic study that has attempted to conduct a quantitative comparison of emergency escape with the laboratory experimental data for the underlying differences in crowd behavior.In this paper, an attempt is made to explore the differences between experimental data on pedestrian crowd egress and emergency egress at a bottleneck and their implication for crowd safety. The laboratory experiments consist of pedestrians passing through a bottleneck of varying widths. The emergency egress data has been extracted from the publicly available rare video footage of panic escape at a shopping center during an Earthquake in China. The extracted data are then used to test a force-based crowd simulation model.It was found that there are underlying differences on the crowd egress behavior (headway distribution and flow) under emergency conditions as compared to controlled laboratory experiment. There is significant number of group exits and less lone exits in emergency egress. It was observed that the force-based model was able to replicate the normal egress as well as panic egress. It is recommended that any pedestrian crowd evacuation simulation model be tested to reproduce this fundamental headway distribution as observed in this study which includes >85% of headway as short headway (≤0.5s) with predominately group exits (0–0.1s headway) rather than lone exits for the bottleneck widths between 1.7 and 2.1m.

TIME HEADWAY ANALYSIS TO DETERMINE THE ROAD CAPACITY

ABSTRACT: In developed countries, road capacity values derived from time headway is in accordance to their local traffic characteristics. In theory, time headway standards are developed using statistics models. These standards however, are not necessarily relevant to use in Indonesia. This is because of the differences in traffic conditions and motorists behaviours between those in developed countries and Indonesia. This study is to develop the time headway distribution model and subsequently to determine lionk-road capacity in the city of Denpasar, Bali Province. The study consists of time headway data analysis, model calibration and validation and road capacity values??determination. The study found that normal distribution model fitted the local traffic conditions. Road capacity values are of 2,466 pcus/hour and 2,900 pcus/hour obtained from time headway model and the Indonesian Road Capacity Manual (MKJI) respectively.

Analysis of vehicle headway distribution on multi-lane freeway considering car–truck interaction

The primary objective of this study is to identify the characteristics of vehicle headway on multi-lane freeway under lane management in China considering car–truck interaction. More specifically, the study focused on answering the following two questions: (1) whether the car–truck interaction has impact on headway, that is, headway varies by different leading and following vehicle types and (2) what is the best-fitted distribution model for particular headway type under lane management. The team collected traffic data, including traffic flow rates, percentage of trucks, speeds, headways, and so on from four segments of Shanghai-Nanjing freeway, Jiangsu Province in China. Then, some statistical methods were used to analyze the vehicle headway. It was found that car–car, car/truck, and truck–truck headways are significantly different from each other. Also, the traffic flow rate, percentage of trucks, and lane position were found to have an influence on the vehicle headway through the tests. Using the maximum-likelihood estimation, Kolmogorov–Smirnov test, and chi-square test techniques, the distribution models and parameter functions for each headway type were built and validated. The results showed that lognormal model is suitable for car–car and truck–truck headway types, and inverse Gaussian model fits the car/truck headway type well.

ANALYSIS OF CAR FOLLOWING HEADWAY ALONG MULTILANE HIGHWAY

This study describes driver’s car following headway on multilane highways. The aim of this study is to analyse the driver’s car following headway along multilane highway at four selected locations. The objectives of this study were to determine car headway at Jalan Batu Pahat – Ayer Hitam multilane highway and to develop linear regression models to present the relationships between headway and speed. Videotaping method was used in field data collection during peak hours. Data were extracted from recorded video by using the image processing technique software. The distance headways and associated vehicles speeds were classified into vehicle following category by vehicle type: car following car, car following heavy goods vehicle, heavy goods vehicle following heavy goods vehicle and heavy goods vehicle following car categories. Linear regressions models were used to develop the relationships between headway and speed. Based on all headway distribution, it is found that patterns of the vehicle headways at four study locations were similar, which shown a significant number of the vehicles travel at headways less than 5 seconds. Furthermore, it can be concluded that many drivers tend to follow the vehicles ahead closely on multilane highways. The regression models were significantly reliable based on their R-square values which are ranging between 0.80 and 0.95. From the analysis, cars were found to maintain larger headways when following heavy goods vehicles compare to when following other cars.

Solving Engineering, Project, and Production Management Problems through Modeling

“Impact Analysis of Headway Distributions on Single-Lane Roundabout Entry Capacity” by Liang Ren and Xiaobo Qu from Australia’s Griffith University was awarded Best Paper Award at the 2015 (6th) International Conference on Engineering, Project, and Production Management, held in Gold Coast, Australia. Here, the paper has been extended to provide additional detail about entry capacity estimation for single-lane roundabouts. The authors present a capacity model which provides improved accuracy over current models.

Impact Analysis of Headway Distributions on Single-Lane Roundabout Entry Capacity

Impact Analysis of Headway Distributions on Single-Lane Roundabout Entry Capacity

Study on Speed and Time-headway Distributions on Two-lane Bidirectional Road in Heterogeneous Traffic Condition

In the present paper an attempt has been made to have an idea about speed and headway distribution pattern in heterogeneous traffic condition comprising of various motorized and non-motorized vehicles having widely varying speed range. Distribution of speed and time headway has been studied for different density levels namely, 0-20 PCU/km, 20-40 PCU/km, 40-60 PCU/km and 60-80 PCU/km. Statistical validity of each distribution is evaluated by Kolmogorov-Smirnov (K-S) test. Results show that the speed and time headway follow different distribution patterns under different density levels. Moreover speed distribution profile is evaluated for different types of vehicle and time headway distribution profiles are also determined for different vehicle pairs. The findings can be used for developing simulation models for two-way, two-lane roads under heterogeneous conditions.

Insights Toward Characteristics of Merging Streams of Pedestrian Crowds Based on Experiments with Panicked Ants

Geometric design of egress and ingress configurations affects collective movement of pedestrians. Merging streams of pedestrian crowds is, in particular, one of the frequently observed features in public infrastructures and mass gatherings. However, few qualitative and quantitative studies have addressed this phenomenon in emergency situations because of the scarcity of data on human panic conditions. This paper studies the underlying geometric factors that affect dynamics and flow characteristics of merging streams in panic conditions through the use of nonhuman entities. Many experiments with panicked ants were performed in different angles and geometric characteristics. Flow rates, headway distributions, and escape speed of merging streams were studied. Results suggest that merging layouts can lead to the creation of stop-and-go phenomena and cause significant variation in the velocities of the joining paths over time. The authors also found that setups with tributary merging paths, in which a deviated stream joins a main branch, performed poorly compared with equivalent symmetrical setups. In addition, results show a dependency between traffic flow characteristics of the merged flow and the merging angle. Analyses also suggest nonexistence of a monotonic relation (or trend) between the merging angle and the merging throughput. This outcome specifically highlights the possibility of the presence of certain merging angles below and above which the overall flow performance is poorer (i.e., optimal angles). The findings provide a better understanding of the macroscopic characteristics of escaping flows in merging sections.

Revised Raff’s Method for Estimating Critical Gaps

The estimation of the critical gap was introduced in the 1970s to evaluate the capacity of vehicle and pedestrian movements at unsignalized intersections. The critical gap is the smallest gap that a driver is assumed to accept. The population of drivers, each with his or her own critical gap, will have a distribution of critical gaps; and it is this distribution, or its characteristics, that is the subject of this paper. These statistics for the critical gap are difficult to estimate; several methods have been developed and used. Raff’s method has been frequently used because of its simplicity. This paper examines the original method, an adaptation of the method that is frequently used, and a proposed adaptation of the method. Simplified traffic and driver behavior characterizations are used to demonstrate the ability of each process to predict the mean critical gap. When given exponential headways in the major stream and a uniform distribution of headways, unbiased estimates of the critical gap would be obtained by using a modified version of Raff’s method involving the accepted gap and the maximum rejected gap. The mean critical gaps estimated with a modified Raff’s method using the maximum rejected gap are slightly inferior to those from the maximum likelihood method. It is recommended that the maximum likelihood method be the preferred technique; it was used in measuring values for the Highway Capacity Manual. However, the modified Raff technique is an acceptable alternative.

Speed and Time Headway Distribution under Mixed Traffic Condition

Time headway and speed distribution studies provide an insight into the aggregate flow of vehicles which have important applications in capacity estimation, Level of Service (LOS) analysis, safety analysis, etc. Analysis of time headways and speed of vehicles were conducted on the basis of data collected from four two-lane bidirectional roads in Assam, India by video recording technique. The paper intends to study time headway distribution of vehicles for the mixed vehicular flow and for different leader-follower vehicle pairs on the basis of six traffic flow levels [0-200, 200-400, 400-600, 600-800, 800-1000 and 1000-1200] PCU/h. Analysis of collected speed data is also carried out to obtain the speed distribution patterns in mixed traffic condition and also vehicle class-wise speed analysis is performed to identify the impact of overall flow and vehicle composition on speed. The results of this paper can find direct applications in developing micro-simulation models.

Robust stop-skipping patterns in urban railway operations under traffic alteration situation

In this paper an operation mode which is based on the stop-skipping approach is studied in urban railway lines under uncertainty. In this mode, each train follows a specific stop schedule. Trains are allowed to skip any intermediate stations to increase the commercial speed and to save energy consumption. As the commercial speed increases, the number of required trains in operation reduces and results eliminating unnecessary costs. To that end, a new mathematical model is proposed to reach the optimum stop schedule patterns. In the planning step, based on the traffic studies, the headway distributions are computed for different weekdays, and holidays. However, in practice, because of many unexpected events, the traffic may alter from what is planned. Therefore, in this condition, a robust plan is required that is optimized and immunized from uncertainty. In this paper, a new robust mathematical model, as well as two heuristic algorithms including (1) a decomposition-based algorithm and (2) a Simulated Annealing (SA) based algorithm is proposed. Finally, an Iranian metro line is studied and the optimum patterns are presented and analyzed.

GIS를 이용한 미시적 수준의 교통모형 구현에 관한 연구

This study aims to design and implement a traffic model that can simulate the traffic behavior on the microscopic level by using the GIS. In the design of the model, the vehicle in the simulation environment recognizes the GIS road centerline data as road network data reflecting number of lanes, speed limit and so on. In addition, the behavior model was designed by dividing functions into the environmental perception model, time headway distribution model, car following model, and lane changing model. The implemented model was applied to Jahamun-road of Jongno-gu district to verify the accuracy of the model. As a result, the simulation results on the Jahamun-road had no great error compared with the actual observation data. In the aspect of usability of model, it is judged that this model will be able to effectively contribute to analysis of amount of carbon emission by traffic, evaluation of traffic flow, plans for location of urban infrastructure and so on.

Revisiting distribution model of departure headways at signalised intersections

ABSTRACTThe departure headway is one of the critical parameters to optimise and evaluate the design and timing of signalised intersections. In order to provide a suitable method to accurately estimate saturation headway at signalised intersections, the distribution of departure headways and its characteristics were investigated based on field observation in Shanghai, China. Statistical analysis results reveal that (1) Shifted Log-Normal distribution can be used to capture the features of departure headways distribution at each position in a queue, including headways at the first position which are usually excluded in existing models; (2)Shifted Log-Normal is more suitable to capture the distribution of steady-flow headways which are approximately the headways at positions between the fifth vehicle and the last stopping vehicle in the queue; (3) the mode of steady-flow headway distribution, which reflects the real manipulative ability of drivers in a certain region, can be considered as theoretical saturation headway and the mean can be considered as practical saturation headway which is used for actual capacity analysis in practice; and (4) saturation headway distribution obeys four-sigma rule. These findings about departure headway distribution at signalised intersections will be helpful for driving behaviour understanding, capacity calculation, design, timing, as well as microscopic traffic simulation of signalised intersections.

Nonparametric Modeling of Vehicle-Type-Specific Headway Distribution in Freeway Work Zones

AbstractThis paper presents a vehicle-type-specific headway distribution analysis in a freeway work zone. The goal of this paper is to provide a vehicle-type-specific model with different time periods using empirical work-zone data from highway I-91 in Greenfield, MA. A nonparametric approach with a Gaussian kernel is used to describe the vehicle-type-specific headway distribution in a freeway work zone. No assumption is required on how the headways should be distributed for nonparametric methods. The vehicles are classified into Car, Van, and Truck based on a FHWA vehicle-type classification scheme. Statistical tests indicate nonparametric distribution with Gaussian kernel outperforms the lognormal distribution in statistical sense according to the χ2 values. Further, another work zone dataset from Jacksonville, FL is utilized to examine the mixed headway scenario without specifying vehicle types. The K−S and Chi-square test results suggest the necessity of considering the vehicle types separately. Follo...

Safety and Headway Characteristics in Highway Work Zones with Automated Speed Enforcement

This paper investigated the headway distribution of platooning vehicles in work zones with and without automated Speed Photo Enforcement (SPE). Data from two work zones were collected and analyzed. The portion of vehicles traveling with a very short headway (less than 0.7 sec) was also examined. In addition, the behavior of vehicles near the law enforcement vehicles was analyzed in terms of applying brakes and changing lane in one of the work zones. The results indicated that the mean headway of cars in the median lane significantly increased in both work zones when the SPE van was present compared to the base condition. For trucks, the mean headway increase was significant only in the shoulder lane when the SPE was present. This is a beneficial effect and indicates that drivers had a longer time to react to the lead vehicles. It was also found that the proportion of cars traveling with a very short headway in the median lane significantly decreased when a SPE van was present at one work zone (I-64). In the shoulder lane, no very short headway was observed when SPE was implemented. The difference in braking behavior was not significant when SPE was compared to police car presence. However, lane changing behavior was significantly different for cars traveling in the median lane and also for trucks traveling in the shoulder lane. The proportion of cars changing lanes was 5 percent with a police car present and increased to 8 percent when the SPE van was present. A significant number of trucks changed lanes from the shoulder to the median when the police car was present to comply with state law.

Effect of minimum headway distance on connectivity of VANETs

The knowledge of vehicle headway distribution is essential for estimating the probability of connectivity in vehicle ad hoc networks. We consider the distribution of vehicles in a single lane, taking into account that consecutive vehicles have to maintain a minimum safe distance between them. It is shown that the account of safe distance improves the agreement between vehicles theoretical spacing distribution and empirical data in single lane traffic. We study how this minimum distance affects the connectivity probability in light traffic conditions. We show that the headway distribution of single lane traffic in the free flow conditions is better modeled using a shifted exponential model which takes into account the safe distance between vehicles. We also show that neglecting this effect will result in overestimating the connectivity in vehicular ad hoc networks, therefore, underestimating the communication range needed to establish the network with a given connectivity probability. The effect is stronger for shorter transmission range.

Vehicle-to-vehicle connectivity on parallel roadways with large road separation

This paper studies vehicle multihop connectivity of vehicular ad hoc networks (VANETs) on two parallel roads. It complements our earlier studies by considering a road separation distance larger than 32L and considering signal blockage between roads, where L represents the transmission range. Assuming vehicles follow Poisson processes, we specifically derive exact formulas for the expectation, variance, and probability distribution of the information propagation distance. We further develop a closed form approximation for the expected distance. The analytical results are verified and compared with those from other headway distributions of varying coefficient of variation through Monte Carlo simulation.

Absence of jamming in ant trails: feedback control of self-propulsion and noise.

We present a model of ant traffic considering individual ants as self-propelled particles undergoing single-file motion on a one-dimensional trail. Recent experiments on unidirectional ant traffic in well-formed natural trails showed that the collective velocity of ants remains approximately unchanged, leading to the absence of jamming even at very high densities [John et al., Phys. Rev. Lett. 102, 108001 (2009)]. Assuming a feedback control mechanism of self-propulsion force generated by each ant using information about the distance from the ant in front, our model captures all the main features observed in the experiment. The distance headway distribution shows a maximum corresponding to separations within clusters. The position of this maximum remains independent of average number density. We find a non-equilibrium first-order transition, with the formation of an infinite cluster at a threshold density where all the ants in the system suddenly become part of a single cluster.