Neural network modeling of vehicle discharge headway at signalized intersection: model descriptions and results

Vehicle discharge headway at signalized intersections is of great importance in junction analysis. However, it is very difficult to simulate the discharge headway of individual queued vehicle because of the great variations in the driver behaviors, vehicle characteristics and traffic environment. The current study proposes a neural network (NN) approach to simulate the queued vehicle discharge headway. A computer-based three-layered (NN) model was developed for the estimation of discharge headway. The widely used backpropagation algorithm has been utilized in training the NN model. The NN model was trained, validated with field data and then compared with other headway models. It was found that the NN model performed better. Model sensitivity analysis was conducted to further validate the applicability of the model. Results showed that the NN model could produce reasonable discharge headway estimates for individual vehicles.     

Passenger car units in saturation flows: Concept,definition, derivation

Passenger car units (pcus) are traditionally used to represent the effects of changes in traffic composition (the mix of cars, goods vehicles, buses, ad so on) on the saturation flows at traffic signal junctions. This paper describes in the results obtained by the two main methods of derivation of pcu values, regression analysis of asynchronous vehicles counts (asynchronous regression) and headway ratio methods, when applied to data from two large public road studies. The relationship between the various methods of derivation used is investigated. Regression analysis of synchronous vehicle counts, Webster's method, and headway ratio methods are seen to agree, but asynchronous regression necessarily gives lower results so long as there is variability in the headways of vehicles of a given class (e.g. in car-to-car headways). Alternative method of regression analysis of asynchronous counts is investigated but found to be biased, although les so than the existing method. Conventional asynchronous regression gives unbiased saturation flow estimates if unbiased prior pcu values are used. The effects of assumed pcu values on signal settings and consequent delays in subsaturation conditions are examined. Value corresponding to delay-minimising settings are close to the ratio of the mean headways of the appropriate vehicle classes.     

Impact of stop-and-go waves and lane changes on discharge rate in recovery flow

In an effort to uncover traffic conditions that trigger discharge rate reductions near active bottlenecks, this paper analyzed individual vehicle trajectories at a microscopic level and documented the findings. Based on an investigation of traffic flow involving diverse traffic situations, a driver’s tendency to take a significant headway after passing stop-and-go waves was identified as one of the influencing factors for discharge rate reduction. Conversely, the pattern of lane changers caused a transient increase in the discharge rate until the situation was relaxed after completing the lane-changing event. Although we observed a high flow from the incoming lane changers, the events ultimately caused adverse impacts on the traffic such that the disturbances generated stop-and-go waves. Based on this observation, we regard upstream lane changes and stop-and-go waves as the responsible factors for the decreased capacity at downstream of active bottlenecks. This empirical investigation also supports the resignation effect, the regressive effect, and the asymmetric behavioral models in differentiating acceleration and deceleration behaviors.     

The capacity of a priority intersection

We present simple formulae for the maximum capacity of an intersection of a single stream of minor traffic with a single stream of major (priority) traffic. The method allows for both mixed (nonhomogeneous) vehicle types and for inconsistent driver behaviour in the minor traffic stream. For a realistic class of major headway distributions the capacity is the harmonic mean of the capacities for each individual vehicle type. The formulae include generalisations of Tanner's formula for the cases of inconsistent and/or nonhomogeneous minor vehicles.     

Effects of countdown timers on queue discharge characteristics of through movement at a signalized intersection

This study investigates how countdown timers installed at a signalized intersection affect the queue discharge characteristics of through movement during the green phase. Since the countdown timers display the time remaining (in seconds) until the onset of the green phase, drivers waiting in the queue at the intersection are aware of the upcoming phase change, and are likely to respond quicker. Thus, the countdown timers could reduce the start-up lost time, decrease the saturation headway, and increase the saturation flow rate. This study observed vehicle flow at an intersection in Bangkok for 24 h when the countdown timers were operating, and for another 24 h when the countdown timers were switched off. The signal plans and timings remained unchanged in both cases. Standard statistical t-tests were used to compare the difference in traffic characteristics between the “with timer” and “without timer” cases. It was found that the countdown timers had a significant impact on the start-up lost time, reducing it by 1.00–1.92 s per cycle, or a 17–32% time saving. However, the effects on saturation headway were found to be trivial, which implies that the countdown timers do not have much impact on the saturation flow rate of signalized intersections, especially during the off-peak day period and the late night period. The savings in the start-up lost time from the countdown timers was estimated to be equivalent to an 8–24 vehicles/h increase for each through movement lane at the intersection being studied.     

Connecting e-hailing to mass transit platform: Analysis of relative spatial position

This paper analyzes and compares two different relative spatial position (RSP) designs in an integrated e-hailing/fixed-route transit system: a zone-based design that operates e-hailing vehicles within a zone, and a line-based design that operates e-hailing vehicles along a fixed-route transit line and with a stable headway. To conduct a meaningful comparison, the optimal design problems for both systems are formulated using a same analytical framework based on the continuous approximation approach. A comprehensive numerical experiment is performed to compare various cost components corresponding to the optimal designs, and a discrete-event simulation model is developed to validate the analysis. The analytical and simulation results agree with each other well, with a discrepancy in the total system cost less than 5% in most test scenarios. These results also suggest that the line-based system consistently outperforms the zone-based system in terms of both agency and user costs, for all scenarios tested. Compared to the zone-based design, the line-based design features a sparser fixed-route network (resulting in larger stop spacing) but a higher dispatching frequency. It is concluded that the higher efficiency of the line-based design is likely derived from the strategy of operating e-hailing vehicles with a more regular route/headway structure and allowing ride-sharing.     

Automated transit headway control via adaptive signal priority

This paper reports on a study that developed a next‐generation Transit Signal Priority (TSP) strategy, Adaptive TSP, that controls adaptively transit operations of high frequency routes using traffic signals, thus automating the operations control task and relieving transit agencies of this burden. The underlying algorithm is based on Reinforcement Learning (RL), an emerging Artificial Intelligence method. The developed RL agent is responsible for determining the best duration of each signal phase such that transit vehicles can recover to the scheduled headway taking into consideration practical phase length constraints. A case study was carried out by employing the microscopic traffic simulation software Paramics to simulate transit and traffic operations at one signalized intersection along the King Streetcar route in downtown Toronto. The results show that the control policy learned by the agent could effectively reduce the transit headway deviation and causes smaller disruption to cross street traffic compared with the existing unconditional transit signal priority algorithm.     

Platooning on two-lane two-way highways: An empirical investigation

This paper presents an empirical investigation into platooning on two-lane two-way highways. The main objective is to better understand this phenomenon that has important implications on traffic performance and safety. Field data from three study sites in the state of Montana were used in this study. Separate investigations were performed to examine the relationships among platoon-related variables, namely; time headway, travel speed, and platoon size. The study confirmed that interaction between successive vehicles in the traffic stream generally diminishes beyond a time headway threshold value that fell in the range of 5–7 seconds. Also, the study revealed that very short headways (less than one second) are more associated with aggressive driving and higher speeds than with slow-moving platoons due to lack of passing opportunities. Further, the study found that amount of impedance to traffic is proportional to the size of platoon as evidenced by the relative difference between mean speed of various size platoons and the mean speed of unimpeded vehicles. The study provided other valuable insights into the platooning phenomenon on two-lane highways that are essential in developing a better understanding of traffic operation on two-lane highways.     

Optimal control of headway variation on transit routes

Headway control strategies have been proposed as methods for correcting transit service irregularities and thereby reducing passenger wait times at stops. This paper addresses a particular strategy which can be implemented on high frequency routes (headways under 10–12 minutes), in which buses are held at a control stop to a threshold headway. An algorithm is developed which yields the optimal control stop location and optimal threshold headway with respect to a system wait function. The specification of the wait function is based on the development of several empirical models, including a headway variation model and an average delay time model at control stops. A conclusion is reached that the headway variation does not increase linearly along a route, a common assumption made in many previous studies. Furthermore, the location of the optimal control stop and threshold value are sensitive to the passenger boarding profile, as expected. The algorithm itself appears to have practical application to conventional transit operations.     

Vehicle headway modeling and its inferences in macroscopic/microscopic traffic flow theory: A survey

Vehicle headway distribution models are widely used in traffic engineering fields, since they reflect the fundamental uncertainty in drivers' car-following maneuvers and meanwhile provide a concise way to describe the stochastic feature of traffic flows. This paper presents a systematic review of vehicle headway distribution studies in the last few decades. Since it is impossible to enumerate the merits and drawbacks of all of existing distribution models, we emphasize four advances of headway distribution modeling in this paper. First, we highlight the chronicle of key assumptions on the existing distribution models and explain why this evolution occurs. Second, we show that departure headways measured for interrupted flows on urban streets and headways measured for uninterrupted flows on freeways have common features and can be simulated by a unified microscopic car-following model. The interesting finding helps gather two kinds of headway distribution models under one umbrella. Third, we review different approaches that aim to link microscopic car-following models and mesoscopic vehicle headway distribution models. Fourth, we show that both the point scattering on the density-flow plot and the shape of traffic flow breakdown curve implicitly depend on the vehicular headway distribution. These findings reveal pervasive connections between macroscopic traffic flow models and mesoscopic headway distribution. All these new insights bring new vigor into vehicle headway studies and open research frontiers in this field.     

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. ©     

Distributions of queue lengths at fixed time traffic signals

This paper presents a new model which studies probability distributions of queue lengths at fixed time traffic signals. It extends Haight's model for Poisson arrivals that the arrival distribution during the effective red period is general and the headway between two successive departures is not less than the minimum departure headway. Moreover, the probability generating function of the queue length, at the end of the effective red period, is derived. The probabilities of the queue lengths, at the ends of the effective green, actual red and amber periods, are also obtained. Comparison is made with Haight's model. Finally a case study for the proposed model is reported.     

A capacity model for all-way stop-controlled intersections based on stream interactions

This paper presents a methodology for analyzing the capacity of all-way stop-controlled intersections and the data that have been collected to validate and support the methodology. The rate of departure from one approach of an all-way stop-controlled intersection is controlled by the presence or absence of vehicles on the other approaches. This degree of conflict is classified into a set of unique cases. Field measurements covering over 20,000 vehicle headways were classified into five degree of conflict cases. The model forecasts the mean departure headway based on the probability of occurrence of each degree of conflict case. ©     

A mathematical model for headway variance of fixed-route buses

A mathematical model for computing and analysing headway variance of fixed-route buses offering scheduled service is developed. The model assumes a situation where both the passengers' OD pattern and the bus-route structure do not have any particular form but the number of passengers served at any bus station is a stationary Poisson process. Basic probability concepts are mostly used in deriving the model. Innovations in the model are the inclusion of a skip probability at a stop and the correlation factors between successive bus loads at a loading point and between the travel times of successive buses on a link. The model is, therefore, applicable to a wider range of situations than was possible with the earlier models. Results indicate that bus loading conditions and traffic conditions along the route are the major factors responsible for headway variability. The developed model can be used to determine the relative importance of these factors on headway variance at individual stopping station and thereby simplify the task of evolving effective countermeasures in any given situation. A numerical example that illustrates the application of the model is also given.     

Control of personal rapid transit systems

The problem of precise longitudinal control of vehicles so that they follow predetermined time-varying speeds and positions has been solved. To control vehicles to the required close headway of at least 0.5 sec, the control philosophy is different from but no less rigorous than that of railroad practice. The preferred control strategy is one that could be called an “asynchronous point follower.” Such a strategy requires no clock synchronization, is flexible in all unusual conditions, permits the maximum possible throughput, requires a minimum of maneuvering and uses a minimum of software. Since wayside zone controllers have in their memory exactly the same maneuver equations as the on-board computers, accurate safety monitoring is practical. The paper discusses the functions of vehicle control; the control of station, merge, and diverge zones; and central control.     

Delay-based passenger car equivalents for trucks at signalized intersections

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

The process of information propagation in a traffic stream with a general vehicle headway: A revisit

Effective inter-vehicle communication is fundamental to a decentralized traffic information system based on mobile ad hoc vehicle networks. Here we model the information propagation process through inter-vehicle communication when the vehicle spacing follows a general i.i.d. distribution. Equations for the expected value and variance of propagation distance are derived. In addition, we provide simple equations for the expected number of vehicles covered and the probability distribution of propagation distance. This research advances on an earlier study where the vehicle spacing is assumed to follow an exponential distribution. This paper generalizes the earlier results and potentially enables a design for robust information propagation by allowing for examination of the impact of different headway distributions. Within the new modeling framework, we also compute connectivity between two vehicles.     

Bulk service queues with deviations from departure schedules: The problem of correlated headways

The usual approach to studying bulk service queues is to assume that successive headways are independent. This assumption is frequently violated in systems where vehicles depart according to a fixed schedule, but where deviations from the schedule may occur. A late departure implies there is one long headway followed by a shorter one. This problem is solved exactly using both classical transform techniques and iterative numerical methods. Experiments with the latter approach are presented, and comparisons between the exact results and those obtained by ignoring correlations between headways are performed. The results suggest that upper and lower bounds may be developed using existing results, where the upper bound is accurate in light traffic while the lower bound is accurate in heavy traffic.     

Macroscopic traffic flow propagation stability for adaptive cruise controlled vehicles

Traffic flow propagation stability is concerned about whether a traffic flow perturbation will propagate and form a traffic shockwave. In this paper, we discuss a general approach to the macroscopic traffic flow propagation stability for adaptive cruise controlled (ACC) vehicles. We present a macroscopic model with velocity saturation for traffic flow in which each individual vehicle is controlled by an adaptive cruise control spacing policy. A nonlinear traffic flow stability criterion is investigated using a wavefront expansion technique. Quantitative relationships between traffic flow stability and model parameters (such as traffic flow and speed, etc.) are derived for a generalized ACC traffic flow model. The newly derived stability results are in agreement with previously derived results that were obtained using both microscopic and macroscopic models with a constant time headway (CTH) policy. Moreover, the stability results derived in this paper provide sufficient and necessary conditions for ACC traffic flow stability and can be used to design other ACC spacing policies.     

Mixed manual/semi-automated traffic: a macroscopic analysis

The use of advanced technologies and intelligence in vehicles and infrastructure could make the current highway transportation system much more efficient. Semi-automated vehicles with the capability of automatically following a vehicle in front as long as it is in the same lane and in the vicinity of the forward looking ranging sensor are expected to be deployed in the near future. Their penetration into the current manual traffic will give rise to mixed manual/semi-automated traffic. In this paper, we analyze the fundamental flow–density curve for mixed traffic using flow–density curves for 100% manual and 100% semi-automated traffic. Assuming that semi-automated vehicles use a time headway smaller than today’s manual traffic average due to the use of sensors and actuators, we have shown using the flow–density diagram that the traffic flow rate will increase in mixed traffic. We have also shown that the flow–density curve for mixed traffic is restricted between the flow–density curves for 100% manual and 100% semi-automated traffic. We have presented in a graphical way that the presence of semi-automated vehicles in mixed traffic propagates a shock wave faster than in manual traffic. We have demonstrated that the presence of semi-automated vehicles does not change the total travel time of vehicles in mixed traffic. Though we observed that with 50% semi-automated vehicles a vehicle travels 10.6% more distance than a vehicle in manual traffic for the same time horizon and starting at approximately the same position, this increase is marginal and is within the modeling error. Lastly, we have shown that when shock waves on the highway produce stop-and-go traffic, the average delay experienced by vehicles at standstill is lower in mixed traffic than in manual traffic, while the average number of vehicles at standstill remains unchanged.