Improved driver responses at intersections with red signal countdown timers

Traffic Signal Countdown Timers (TSCTs) are innovative, practical and cost effective technologies with the potential to improve efficiency at signalized intersections. The purpose of these devices is to assist motorists in decision-making at signalized intersections with real-time signal duration information. This study focused specifically on driver responses in the presence of a Red Signal Countdown Timer (RSCT). A Linear Mixed Effect (LME) model was developed to predict the effect of RSCT on the headway of the first vehicle waiting on a red signal. The model predicted 0.72 s reduction in the headway of the first queued vehicle resulting from the presence of RSCT, while the observed difference in mean headway was 0.82 s. This result is suggestive of a reduction in start-up lost time at signalized intersections, i.e., an improvement in signalized intersection efficiency when an RSCT is present.     

Discharge headway at signalized intersections in Hong Kong

This paper reports the analysis and comparisons of discharge headways at 26 sites in Hong Kong. Previous studies here established good understanding of the average discharge headway under various conditions but very few studies dealt with discharge headway of individual vehicles which is a vital component in the traffic simulation at signalized intersections. This study that looked into the discharge headway of individual vehicles found that the discharge headway at different queue position follows the Type I Extreme Value Distribution. A method of estimating site‐specific parameters for this distribution has also been proposed.     

Optimizing fare and headway to facilitate timed transfer considering demand elasticity

Fare and service frequency significantly affect transit users’ willingness to ride, as well as the supplier's revenue and operating costs. To stimulate demand and increase productivity, it is desirable to reduce the transfer time from one route to another via efficient service coordination, such as timed transfer. Since demand varies both temporally and spatially, it may not be cost-effective to synchronize vehicle arrivals on all connecting routes at a terminal. In this paper, we develop a schedule coordination model to optimize fare and headway considering demand elasticity. The headway of each route is treated as an integer-multiple of a base common headway. A discounted (reduced) fare is applied as an incentive to encourage ridership and, thus, stimulate public transit usage. The objective of the proposed coordination model is used to maximize the total profit subject to the service constraint. A numerical example is given to demonstrate the applicability of the proposed model. The results show that the optimized fare and headway may be carefully applied to yield the maximum profit. The relationship between the decision variables and model parameters is explored in the sensitivity analysis.     

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.     

An observed traffic pattern in long freeway queues

A simple exercise in data analysis showed that, in queued traffic, a well-defined relation exists between the flow on a homogeneous freeway segment and the segment’s vehicle accumulation. The exercise consisted of constructing cumulative vehicle arrival curves to measure the flows and densities on multiple segments of a queued freeway. At this particular site, each interchange enveloped by the queue exhibited a higher on-ramp flow than off-ramp flow and as a consequence, motorists encountered a steady improvement in traffic conditions (e.g., reduced densities and increased speeds) as they traveled from the tail of the queue to the bottleneck. This finding has practical implications for freeway traffic planning and management. Perhaps most notably, it suggests that the first-order hydrodynamic theory of traffic is adequate for describing some of the more relevant features of queue evolution. This and other practical issues are discussed in some detail.     

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.     

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.     

A connected-vehicle-based dynamic control model for managing the bus bunching problem with capacity constraints

This paper describes a connected-vehicle-based system architecture which can provide more precise and comprehensive information on bus movements and passenger status. Then a dynamic control method is proposed using connected vehicle data. Traditionally, the bus bunching problem has been formulated into one of two types of optimization problem. The first uses total passenger time cost as the objective function and capacity, safe headway, and other factors as constraints. Due to the large number of scenarios considered, this type of framework is inefficient for real-time implementation. The other type uses headway adherence as the objective and applies a feedback control framework to minimize headway variations. Due to the simplicity in the formulation and solution algorithms, the headway-based models are more suitable for real-time transit operations. However, the headway-based feedback control framework proposed in the literature still assumes homogeneous conditions at all bus stations, and does not consider restricting passenger loads within the capacity constraints. In this paper, a dynamic control framework is proposed to improve not only headway adherence but also maintain the stability of passenger load within bus capacity in both homogenous and heterogeneous situations at bus stations. The study provides the stability conditions for optimal control with heterogeneous bus conditions and derives optimal control strategies to minimize passenger transit cost while maintaining vehicle loading within capacity constraints. The proposed model is validated with a numerical analysis and case study based on field data collected in Chengdu, China. The results show that the proposed model performs well on high-demand bus routes.     

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.     

Some observed details of freeway traffic evolution

Certain details of traffic evolution were studied along a 2 km, homogenous freeway segment located upstream of a bottleneck. By comparing (transformed) cumulative curves constructed from the vehicle counts measured at neighboring loop detectors, it was found that waves propagated through queued traffic like a random walk with predictable statistical variation. There was no observed dependency of wave speed on flow. As such, these waves neither focused nor fanned outward and shocks arose only at the interfaces between free-flowing traffic and the back of queues. Although these traffic features may have long been suspected, actual observations of this kind have hitherto not been documented. Also of note, the shocks separating queued and unqueued traffic sometimes exhibited unexpectedly long transitions between these two states. Finally, some observations presented here corroborate earlier reports that, in unqueued traffic, vehicle velocity is insensitive to flows and that forward-moving changes in traffic states therefore travel with vehicles. Taken together, these findings suggest that certain rather simple models suffice for describing traffic on homogeneous freeway segments; brief discussion of this is offered in Section 5.     

Some observed queue discharge features at a freeway bottleneck downstream of a merge

Details of traffic evolution were studied upstream and downstream of a freeway bottleneck located near a busy on-ramp. It is shown that on certain days the bottleneck became active upon dissipation of a queue emanating from somewhere further downstream. On such occasions, the bottleneck occurred at a fixed location, approximately one kilometer downstream of the merge. Notably, even after the dissipation of a downstream queue, the discharge flows in the active bottleneck were nearly constant, since the cumulative counts never deviated much from a linear trend. The average bottleneck discharge flows were also reproducible from day to day. The diagnostic tools used in this study were curves of cumulative vehicle arrival number versus time and cumulative occupancy versus time constructed from data measured at neighboring freeway loop detectors. Once suitably transformed, these cumulative curves provided the measurement resolution necessary to observe the transitions between freely flowing and queued conditions and to identify some important traffic features.     

Analyzing fluctuations in car-following

Many car-following models predict a stable car-following behavior with a very small fluctuation around an equilibrium value g¹ of the net headway g with zero speed-difference Δv between the following and the lead vehicle. However, it is well-known and additionally demonstrated by data in this paper, that the fluctuations are much larger than these models predict. Typically, the fluctuation in speed difference is around ±2 m/s, while the fluctuation in the net time headway T = g/v can be as big as one or even two seconds, which is as large as the mean time headway itself. By analyzing data from loop detectors as well as data from vehicle trajectories, evidence is provided that this randomness is not due to driver heterogeneity, but can be attributed to an internal stochasticity of the driver itself. A final model-based analysis supports the hypothesis, that the preferred headway of the driver is the parameter that is not kept constant but fluctuates strongly, thus causing the even macroscopically observable randomness in traffic flow.     

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.     

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.     

Bus control strategies in corridors with signalized intersections

This paper proposes a new dynamic bus control strategy aimed at reducing the negative effects of time-headway variations on route performance, based on real-time bus tracking data at stops. In routes with high demand, any delay of a single vehicle ends up causing an unstable motion of buses and producing the bus bunching phenomena. This strategy controls the cruising speed of buses and considers the extension of the green phase of traffic lights at intersections, when a bus is significantly delayed. The performance of this strategy will be compared to the current static operation technique based on the provision of slack times at holding points. An operational model is presented in order to estimate the effects of each controlling strategy, taking into account the vehicle capacity constraint. Control strategies are assessed in terms of passenger total travel time, operating cost as well as on the coefficient of headway variation. The effects of controlling strategies are tested in an idealized bus route under different operational settings and in the bus route of highest demand in Barcelona by simulation. The results show that the proposed dynamic controlling strategy reduces total system cost (user and agency) by 15–40% as well as the coefficient of headway variation 53–78% regarding the uncontrolled case, providing a bus performance similar to the expected when time disturbance is not presented.     

Recursive estimation of average vehicle time headway using single inductive loop detector data

Vehicle time headway is an important traffic parameter. It affects roadway safety, capacity, and level of service. Single inductive loop detectors are widely deployed in road networks, supplying a wealth of information on the current status of traffic flow. In this paper, we perform Bayesian analysis to online estimate average vehicle time headway using the data collected from a single inductive loop detector. We consider three different scenarios, i.e. light, congested, and disturbed traffic conditions, and have developed a set of unified recursive estimation equations that can be applied to all three scenarios. The computational overhead of updating the estimate is kept to a minimum. The developed recursive method provides an efficient way for the online monitoring of roadway safety and level of service. The method is illustrated using a simulation study and real traffic data.     

A stochastic model of traffic flow: Theoretical foundations

In a variety of applications of traffic flow, including traffic simulation, real-time estimation and prediction, one requires a probabilistic model of traffic flow. The usual approach to constructing such models involves the addition of random noise terms to deterministic equations, which could lead to negative traffic densities and mean dynamics that are inconsistent with the original deterministic dynamics. This paper offers a new stochastic model of traffic flow that addresses these issues. The source of randomness in the proposed model is the uncertainty inherent in driver gap choice, which is represented by random state dependent vehicle time headways. A wide range of time headway distributions is allowed. From the random time headways, counting processes are defined, which represent cumulative flows across cell boundaries in a discrete space and continuous time conservation framework. We show that our construction implicitly ensures non-negativity of traffic densities and that the fluid limit of the stochastic model is consistent with cell transmission model (CTM) based deterministic dynamics.     

Documents

Automated short headway urban transportation systems were viewed in the early Seventies as a possible means of effecting radical change in the type of transit service available in cities. However, interest has declined and government‐sponsored efforts in this area have ceased. The decline in interest was accompanied by much debate among the advocates of the various forms of transit. However, it does not appear to reflect the potential merits and limitations of short headway systems as disclosed by analysis.

This paper provides a basis for comparing short headway systems of citywide scale with conventional transit means.

The limitations inherent in rapid rail installations are reviewed and contrasted with the performance of short headway systems. Illustrative, large‐scale guideway configurations for systems operating in the three‐second headway range are defined and levels of service are deduced using simplified heuristic methods. A basis is provided for specification and analysis of systems conforming to realistic spatial and passenger‐movement constraints.

It is concluded that automated transit systems operating in the three‐second headway range remain viable candidates for large‐scale installations.     

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.