Systems and methods for detecting traffic conflicts

Abstract

Provided herein are systems and methods for analyzing traffic within an intersection. In particular, provided herein are systems and methods for detecting traffic conflicts between approaching vehicles within an intersection.

Description

SYSTEMS AND METHODS FOR DETECTING TRAFFIC CONFLICTSTECHNOLOGICAL FIELD

[0001] The presently disclosed subject matter relates to systems and methods for analyzing traffic within an intersection. In particular, it relates to systems and methods for detecting instant traffic conflicts between approaching vehicles within an intersection.BACKGROUND

[0002] Traffic conflicts, sometimes referred to as a “near miss." refer to a situation when conflict vehicles are about to crash but the drivers take evasive actions to avoid. Previous research reveals a strong correlation between frequent traffic conflicts and actual crashes. Therefore, it is desired to use the number of identified traffic conflicts as a proactive indicator of crash possibility.

[0003] There are two facets of traffic conflicts: occurrences and severity. Occurrences mean how often the traffic conflicts occur. If they occur frequently at an intersection, then crashes are imminent, and mitigating measures should be implemented immediately; severity means how fatal or harmful if a traffic conflict becomes a real crash. Severe traffic conflicts should also be paid attention to immediately even if they are relatively fewer than less severe traffic conflicts. The crash mitigation measures at signalized intersections can be “responsive’7, according to the captured, estimated traffic conflicts in the immediate past (e.g., in the past 5 minutes), or “adaptive” according to the predicted traffic conflicts shortly (e.g., in the next 5 minutes). The crash mitigation measures can be further defined as “collective” or “instantaneous”. A collective measure means responding to the overall crash risks while an instantaneous measure responds to an identified or predicted near-miss event. In analogy, the collective measures as opposed to actuated measures are like atime-of-day traffic signal timing plan for varying travel demands vs. a dynamic all-red extension to prevent a red-light runner from crashing. Previous research on realtime crash risk prediction can serve as the foundation of a “collective” approach to cash risk reduction. On the other hand, only limited research on “instantaneous” traffic conflict identification and crash prediction for certain instantaneous crash mitigations has been conducted.

[0004] Traffic conflicts refer to potential crash situations when conflict vehicles are in an imminent situation of collision but take evasive actions to avoid it. The concept of traffic conflicts can be traced back to 1968 when Perkins and Harris (Highway Transportation Record, (1968) 225:35) from General Motors observed and summarized traffic conflicts at intersections. Other early studies include Older and Spicer (Human factors (1976) 18:335) categorized the observed traffic conflicts at various road locations into different types ; Baker (Highway Research Record, No. 384, 1972) confirmed the close associationbetween traffic conflicts and crashes based on the data collected at 392 intersections and pointed out the benefits of traffic conflict analysis for traffic safety at rural areas; Glauz et al. conducted an extensive survey and summary on traffic conflict analysis and practice in the US (Research Program Report (1980) Vol. 219; Transportation Research Record (1985) 1026:1). Among those early studies, tabulating the numbers and frequencies of observed traffic conflicts and their association with real crashes is the main finding. To reveal the other element of traffic safety, it is required to understand the severity of each traffic conflict. Gettman and Head (Transportation Research Record (2003) 1840:104) summarized seven indicators of near-miss severity: gap time (GT), encroachment time (ET), deceleration rate (DR), the proportion of stopping distance (PSD), post-encroachment time (PET), initially attempted postencroachment time (IAPT) and time to collision (TTC). Among these indicators, TTC and PET are the most popular because they can be easily measured from the vehicle trajectories. As demonstrated in Fig. 1, the difference between TTC and PET is whether the late following vehicle's (v2) deceleration is considered. There are also other variants of TTC, such as the modified time to collision or MTCC due to Ozbay et al. (Transportation Research Record (2008) 2083: 105). The data sources for traffic conflict identification include loop detectors (for longitudinal traffic conflicts), video detection and tracking, radar, or Light Detection and Ranging (LiDAR) detectors. The algorithms used for near-miss identification and prediction include regression, Bayesian, and artificial intelligence techniques, etc. The literature on traffic conflict studies are prolific and still an active research area.

[0005] It becomes increasingly appealing for real-time estimation and prediction of traffic conflicts, rather than using historical data. Being ’‘real-time” is a relative concept. It can refer to (I): A short period like a 5-minute time window or (II): instantaneous when the time window is approaching zero (e.g., less than 0.1 s). Achieving instantaneous identification is challenging and restricted by many factors, such as computing resources and algorithms but it can pave the road for novel safety-centric traffic control strategies. Cai et al. used a microscopic vehicle detection system on freeways to measure vehicles’ longitudinal maneuvers and identify traffic conflicts. They applied a Bayesian multilevel logistic regression to estimate the possibilities of crashes using the Bernoulli distribution. Wang et al. (Accident Analysis & Prevention (2019) 122:378) adopted a similar framework but they considered a more macroscopic feature, such as trip generation and socio-demographic information. Zheng and Sayed (Transportation research part C: emerging technologies (2020) 117:102683.) retrieved vehicle trajectories from video cameras at signalized intersections to identify traffic conflicts and developed a generalized extreme value (GEV) model to predict at intersections. They also derived two new safety' indices, the risk of crash (RC) and the return level of a cycle (RLC). The developed method was validated with observed crashes. Athanasios et al. (Transportation Research Record (2019) 2673:169) used the loop detector data containing vehicle headways and speeds and crash records to generate a training dataset They also applied multiple machine learning and deep learning models to examine various models’ performance and concluded that the deep learning models perform better than the traditional machine learning models in crash prediction. Basso et al. (Accident Analysis & Prevention (2021) 162:106409) used two deep-learning models to capture the nuance difference among vehicles within video detections and developed a training data set to estimate crash potentials. They also adopted oversampling techniques to increase the importance of rare crash data to make the framework more effective. Yuan et al. (Transportation Research Record (2019) pp. 2673:314) applied the deep learning model not only to estimate the crash risk but also to predict the crash risk in the near-term future. They adopted a long short-term memory' recurrent neural network (LSTM-RNN) model and generated the training data set with oversampling techniques for the rare crash data. A feature in preparing the training data is that the input variables include the Bluetooth-based travel time and automated traffic signal performance measure (ATSPM) data. The prediction accuracy is reported as 60%. Li et al. (Accident Analysis <£ Prevention (2020) 135:105371) further enhanced this frameyvork and increased the prediction accuracy up to 88%. Arash and Ahmed (Journal of transportation safety & security. (2022) 14:1165-1200) used the connected vehicle (CV) data and crash record to prepare the data set for training various logistic regression models to predict crashes from a rural CV testbed in Wyoming. The input variables include continuous and categorical ones, most of yvhich were associated with speeds and volumes. To overcome the rare-event nature of crash records, Peng et al. (Traffic injury prevention (2020) 21: 201) adopted the Youden Index method to adjust the classification threshold in the crash prediction models and the experiments show better performance and accuracy than the original data set. Li and Abdel-Aty (Accident Analysis & Prevention (2022) 165:106504) expanded the crash prediction to secondary crashes. Using the spatio-temporal thresholds which are 15 minutes after a crash occurred and up to 1,600 meters from the crash site, secondary crashes are first identified. In the meantime, the corresponding traffic speed, volume, and lane occupancy were collected with roadside detectors on freeyvays. After the training data were generated for the XGBoost model, the reporting accuracy reached 80%. Thapa et al. (Accident Analysis & Prevention (2022) 169:106639) divided road links into cell segments over time. The crash samples are aggregated into cell segments with small time windows. This is a new sampling technique and the results show they can reduce the samples by 25% to achieve a similar performance, interpreted into a reduced computational load. Yu et al. (Transportation research part C: emerging technologies (2020) 119:102740) developed a ney tensor structure to construct the inputs of training data set and adopted refined-focal loss functions for the imbalanced data issue. Using the data collected data, the proposed model obtained 67% accuracy and 4 false alarm rate. Using 28,000 investigation results of frontal vehicle collisions, Wang et al. (Accident Analysis & Prevention (2021) 156:106149) adopted a deep neural network model to extract kinematic features and then predict crashrisk with a support vector machine or SVM model accordingly. The prediction accuracy was reportedly 85.4% with a latency of lower than 1.2 milliseconds. Shuangguan et al. (Accident Analysis & Prevention (2021) 156:106122) predicted crash risks by observing and extracting drivers’ behaviors. Using the naturalistic data set and four machine learning models (XGBoost, SVM, RF, and MLP), drivers’ crash potentials are predicted.

[0006] Thus, a common pattern that is found is that most known methods are driven by big data sets and various regression, machine learning, and deep learning models. The output will be the predicted overall / statist! cal collision risk soon (e.g., 5 minutes ahead) for all vehicles.

[0007] Furthermore, identifying the traffic conflicts is based on conflict vehicles’ maneuvers and therefore it is common to analyze the vehicle trajectories and capture those traffic conflicts. However, this approach faces a few challenges in real-time applications. Identifying traffic conflicts from vehicle trajectories is computing-intensive and so cannot be achieved both quickly and cost-effectively. In the meantime, roadside sensors like video, radar, or LiDAR have inherent positioning errors (e.g., parallax). When vehicles’ speeds are derived by dividing the measured position difference by a small interval like 0.1 s. A small position error can be easily amplified into wrong speed estimation and therefore the nearmiss identification.

[0008] While this information is important to support traffic managers in reducing crashes, it may not necessarily identify' and predict individual imminent crashes and their severity. In the meantime, the realtime traffic conflict events would be a fundamental input for safety-centric traffic signal systems at intersections.

[0009] This invention distinguishes itself by presenting a method to identify instantaneous traffic conflicts and predict crash severity based on state-of-the-art LiDAR-tracked trajectories, including both vehicles and vulnerable road users (VRUs). It is based on high-granular vehicle trajectories but requires little computing resources. These features are expected to pave the road for real-time safety-centric traffic signal control strategies.SUMMARY

[0010] According to an aspect of the presently disclosed subject matter, there is provided a traffic control system configured for being operatively coupled to a traffic signal system, the traffic control system comprising:• a tracking system, comprising one or more tracking sensors configured to identify road users associated with an intersection, and to measure the speeds and locations of identified road users; and• a controller, configured to:o identify two road users associated with the intersection, and measure their instantaneous locations and speeds; o assign the identified road users to a predefined class-pair, the class-pair comprising a classification indicating a type and / or traj ectoiy through the intersection of each of the identified road users; o determine a conflict zone within the intersection for the assigned class-pair; o predict, based on instantaneous measurements by the tracking system of the two identified road users, when each will be within the conflict zone; and o detect a potential traffic conflict when the two identified road users are predicted to be within the conflict zone simultaneously.

[0011] The controller may be further configured to operate the traffic signal system to mitigate the risk of traffic conflicts within the intersection between pairs of road users matching the classifications of the two identified road users.

[0012] Determining the conflict zone within the intersection for the determined class-pair may comprise:• for each classification of the class-pair, assessing the extents of the expected trajectories of road users of within the intersection. wherein the conflict zone comprises a base region of the intersection bounded by the extents of the expected trajectories of the class-pair.

[0013] Assessing the extents of the expected trajectories may comprise monitoring the intersection for a predetermined amount of time and storing trajectory information of road users.

[0014] The conflict zone may further comprise a crash- clearance region, the crash-clearance region being determined such that a first of the identified road users leaves the conflict zone a predetermined amount of time before a second of the identified road users, being a vehicle, reaches the conflict zone without decelerating.

[0015] The conflict zone may further comprise a crash-clearance region, wherein the conflict zone further comprises a crash-clearance region, the crash-clearance region being determined such that a first of the identified road users leaves the conflict zone a predetermined amount of time before a second of the identified road users, being a vehicle, reaches the conflict zone with decelerating.

[0016] The identified road users may be assigned to a class-pair comprising a permissive right-turn vehicle and a vulnerable road user.

[0017] A potential traffic conflict may be detected if the permissive right-turn vehicle is predicted to reach the conflict zone if a predicted stopping distance thereof exceeds a minimum allowable stopping distance.

[0018] The predicted stopping distance may be given by:

[0019] where VR is the speed in m / s of the permissive right-turn vehicle as it passes a stop line entering the intersection, to is a perception-reaction time in seconds, tp is a maximum deceleration rate in m / s2, g is the gravitational acceleration rate in m / s2, and G is the road grade percentage. When speed is expressed in ft / s and acceleration / deceleration rates are expressed in ft / s2, the coefficients 0.278 and 254 should be replaced, respectively, with 1.47 and 30. Herein the specification and appended claims, the road grade percentage is expressed as a positive number for an uphill grade and as negative number for a downhill grade. The gravitational acceleration rate may vary based on location, but in general a value of 9.81 m / s2(32.2 ft / s2) may be used.

[0020] According to some examples, the maximum deceleration rate ip is 3.4 m / s2(11.2 ft / s2), in accordance with the recommendation of the American Association of State Highway and Transportation Officials.

[0021] The shortest allowable stopping distance may be given by:where d\ is the distance from the curb to the centerline of the lane in which the permissive right-turn vehicle approaches the intersection,is the distance from the curb to the centerline of the lane closest to the curb which the vulnerable road user is crossing.

[0022] The identified road users may be assigned to a class-pair comprising a permissive left-turn vehicle and an opposing-through vehicle.

[0023] A potential traffic conflict may be detected if the opposing-through vehicle is predicted to reach the conflict zone while the permissive left-turn vehicle is predicted to be at least partially within the conflict zone.

[0024] The predicted travel distance of the opposing-through vehicle while the permissive left-turn vehicle is at least partially within the conflict zone may be given by:O.278v0t0+vQ-( O-<P fa-tp))225 +c) where vo is the initial speed in m / s of the opposing-through vehicle, to is a perception-reaction time in seconds, fc is the time in seconds during which any part of the permissive left-turn vehicle is predicted to be within the conflict zone, tp is a maximum deceleration rate in m / s2, g is the gravitational acceleration rate in m / s2, and G is the road grade percentage, which is expressed as a positive number for an uphill grade and as negative number for a downhill grade. When speed is expressed in ft / s andacceleration / deceleration rates are expressed in ft / s2, the coefficients 0.278 and 254 should be replaced, respectively, with 1.47 and 30.

[0025] The amount of time fc during which any part of the permissive left-turn vehicle is predicted to be within the conflict zone may be given by:<5(L+w)VL ’ where 8 is an empirical factor which takes into account a predicted curved trajectory of the permissive left-turn vehicle and intersection geometry, L is a vehicle length associated with the permissive left-turn vehicle, w is the total width of all opposing traffic lanes which the permissive left-turn vehicle crosses during its turn, and VL is the speed of the permissive left-turn vehicle.

[0026] The identified road users may be assigned to a class-pair comprising a permissive left-turn vehicle and a vulnerable road user.

[0027] A potential traffic conflict may be detected if the permissive left-turn vehicle and the vulnerable road user are predicted to be in the conflict zone simultaneously.

[0028] The identified road users may be assigned to a class-pair comprising a permissive right-turn vehicle and a U-tum vehicle.

[0029] A potential traffic conflict may be detected if the permissive right-turn vehicle and U-tum vehicle are predicted to be in the conflict zone simultaneously.

[0030] The traffic control system may be further configured to:• identify a road user approaching a signalized intersection and measure its instantaneous location and speed;• determine a red-light conflict zone within the intersection; and• detect a potential traffic conflict if the road user enters the red-light conflict zone when subj ect to a red-light traffic signal indicator.

[0031] The tracking sensors may comprise LiDAR sensors and / or other tracking sensors.BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to better understand the subject matter that is disclosed herein and to exemplify how it may be carried out in practice, embodiments will now be described, by way of non-limiting example only, with reference to the accompanying drawings, in which:

[0033] Fig. 1 schematically illustrates time to collision (TTC) and post-encroachment time (PET) adapted from Gettman and Head {Transportation Research Record (2003) 1840:104).

[0034] Fig. 2 schematically illustrates a system traffic control system according to the presently disclosed subject matter.

[0035] Figs. 3A and 3B illustrate conflict zone determination for a class-pair comprising a permissive left-turn vehicle and an opposing-through vehicle.

[0036] Figs. 4A through 4E illustrate different class-pairs and corresponding conflict zones for each.

[0037] Fig. 5 schematically illustrates safe clearance between two conflict vehicles.

[0038] Fig. 6 schematically illustrates Conflict Zone extension to accommodate TTC and PET.

[0039] Fig. 7 schematically illustrates Extended Conflict Zones to accommodate TTC and PET.

[0040] Fig. 8 illustrates intersection layout for the case study.

[0041] Fig. 9 shows a table showing the format of instantaneously reported traffic conflicts.

[0042] Fig. 10 shows evaluation of LiDAR-reported PETs.DETAILED DESCRIPTION OF EMBODIMENTS

[0043] To address one or more of the above issues, a proximity-based system is presented in this disclosure. The system is based on the notion that a traffic conflict will occur whenever conflicting vehicles are close at dangerously high speeds. The conflict zones are designed in a way that, if conflicting fast vehicles appear in the zone at the same time, they must take evasive maneuvers to avoid collisions, defined as a traffic conflict. Capturing instantaneous traffic conflicts with this system only needs to capture isolated events instead of continuously tracking all vehicles. Therefore, it can be implemented for real-time applications.

[0044] Collisions at intersections occur more frequently than those on highway segments, because there are more traffic conflicts at intersections. Traditional traffic conflict point analysis is the foundation of traffic safety analysis and control design at intersections. While it is commonly accepted, this system in nature ignores vehicles’ lateral maneuvers and drivers' random decisions to change lanes while moving within intersections.

[0045] As illustrated in Fig. 2, the present disclosure provides a traffic control system, which is generally indicated at 10. The traffic control system 10 is configured to monitor road users approaching an intersection, and-based on suitable measured parameters-to detect potential traffic conflicts. The traffic control system 10 may be operatively coupled to a traffic signal system 12, e.g., comprising one or more traffic control indicators associated with road users traversing the intersection along one or more trajectories, for example facilitating operation by the traffic control system of one or more of the traffic control indicators to mitigate a predicted traffic conflict.

[0046] The traffic control system 10 comprises a tracking system 14 and a controller (not illustrated) to direct operation of the traffic control system 10 and to carry out operations and / or methods performed by the traffic control system.

[0047] The tracking system 14 is configured to identify road users associated with the intersection, i.e., those approaching the intersection, in the intersection, etc. In particular, the tracking system 14 is configured to measure the speeds and locations of identified road users in real time, i.e., it takes the measurements immediately, such that they are available to, e.g., immediately, for example before approaching road users reach the intersection.

[0048] The controller may comprise any suitable processor configured to execute instructions and to carry out operations associated with tracking system 10, one or more storage blocks configured to store computer code and / or data, e.g., collected by the tracking system 14. The controller may further comprise one or more display interfaces, one or more input interfaces, one or more network interfaces, etc., all for example as is well-known in the art.

[0049] It will be appreciated that while herein the specification and claims, the term “controller’ ' is used with reference to a single element, it may comprise a combination of elements, which may or may not be in physical proximity7to one another, without departing from the scope of the presently disclosed subject matter, mutatis mutandis. In addition, disclosure herein (including recitation in the appended claims) of the controller carrying out, being configured to carry out, or other similar language, implicitly includes other elements of the traffic control system 10 carrying out, being configured to carry7out, etc., those functions, without departing from the scope of the presently disclosed subject matter, mutatis mutandis.

[0050] The traffic control system 10 is configured to predict, based on measurements performed by the tracking system 14, when two approaching road users will enter a conflict zone of the intersection (determination of the conflict zone will be discussed below). Based on the prediction and other factors, including, but not limited to, predicted trajectories of the road users through the intersection, the types of road users (vehicles, pedestrians, etc.), a potential traffic conflict is detected.

[0051] Relevant factors which are considered during the detection of a potential traffic conflict include, but are not limited to, the trajectories of road users through the intersections. These are often knowable based on the lane of traffic in which vehicles approach the intersection, e.g., whether the vehicle is travelling in a turn-only lane, etc. The traffic control system 10 may be configured to classify each road user approaching an intersection into one of at least the following classifications:• Through vehicle. A vehicle traversing the intersection without turning.• Permissive right-turn vehicle. A vehicle making a right-turn through the intersection, and which is required to first yield to conflicting traffic and / or pedestrians.• Permissive left-turn vehicle. A vehicle making a left-turn through the intersection, and which is required to first yield to conflicting traffic and / or pedestrians.• U-turn vehicle. A vehicle making a U-tum through the intersection.• Vulnerable road user. A road user not protected by a vehicle, often a pedestrian.

[0052] Traffic conflicts can be caused by two types of driver behaviors: (I) Negligence and (II) Misperception. Negligence means that a driver fails to see conflicting vehicles or VRU in time and so they must take evasive actions to avoid collisions; a driver may also misperceive imminent traffic conflicts, causing too small gaps between conflicting vehicles, like during permissive movements or red- light running which is considered a special type of traffic conflict with yellow and clearance. Traffic conflicts due to drivers’ negligence can occur regardless of vehicles’ speeds while the traffic conflicts due to misperception often occur at relatively high speeds. Therefore, the negligence-type traffic conflicts are distinguished from misperception-type traffic conflicts in this disclosure. The traffic conflicts at intersections are grouped as follows:• Traffic conflicts due to negligence: o Permissive right-turn vehicles vs. crossing pedestrians o Permissive right-turn vehicles vs. U-turn vehicles o Permissive left-turn vehicles vs. crossing pedestrians• Traffic conflicts due to misperception: o Permissive left-turn vehicles vs. opposing through vehicles o Red-light running (entering intersections after yellow ends)

[0053] Even though frequent near-misses suggest collision risks, an individual collision may not necessarily be accompanied by a corresponding near-miss occurrence. Near-misses are the result of drivers trying their best to avoid collisions whereas causes of real collisions are more complicated.

[0054] Based on the above, the traffic control system 10 is generally configured to consider potential traffic conflicts between pairs of road users, which may be of different classifications; accordingly, each pair of road users approaching an intersection may be assigned to a class-pair, which is defined by the classifications of the two road users. Accordingly, the traffic control system 10 is configured to apply different methods to detect potential traffic conflicts for different class-pairs.

[0055] Examples of class-pairs which the traffic control system 10 may be configured to consider include, but are not limited to:• a permissive right-turn vehicle and a vulnerable road user;• a permissive left-turn vehicle and an opposing-through vehicle;• a permissive left-turn vehicle and a vulnerable road user; and• a permissive right-turn vehicle and a U-turn vehicle.

[0056] For each of the class-pairs, the traffic control system 10 is configured to determine a corresponding conflict zone. In general, conflict zones are selected such that if two road users appearin the zone at the same time, in particular if at least one is moving at a high speed, one or more would have to make evasive maneuvers to avoid a collision, giving rise to a traffic conflict, sometimes referred to as a ‘‘near miss.” The traffic control system 10, using measurements from the tracking system 14 and analysis based on conflict zones, may thus detect traffic conflicts in real time using a small amount of information about selected road users, thereby reducing the required equipment and necessary processing power which would be needed to make similar detections based on continuously tracking all road users.

[0057] The traffic control system 10 is configured to determine conflict zones for the intersection for a given class-pair based on aggregated behavior of road users. According to some examples, the traffic control system 10 is configured to gather data regarding the paths which road users take through the intersection. From this data, it selects all the paths taken by road users of a classification, and identifies the extents thereof, i.e., the paths between which substantially all (e.g., ignoring outliers) other paths taken by road users of the same class he.

[0058] Fig. 3A demonstrates one of the conflict zones between permissive left-turn vehicles and opposing through vehicles. In the real world, approaching vehicles make random maneuvers within intersections, creating '‘conflict zones” instead of “conflict points”. Fig. 3B is a trace of 1 % of an hour of LiDAR-tracked trajectories of all approaching vehicles at an intersection. It clearly shows the inherent lateral vehicle maneuvers and the existence of “conflict zones”. Traditional conflict points are likely within the corresponding conflict zones. Traffic conflict occurs when conflicting vehicles appear in the conflict zone (i.e., dangerously close) at high speeds. Not all traffic conflicts will lead to real crashes because drivers will mostly take evasive actions to avoid them with success.

[0059] Accordingly, as illustrated in Figs. 3 A and 3B, the tracking system 14 may track road users traversing the intersection for a predetermined time period. To determine a conflict zone 16 for a class-pair comprising a permissive left-turn vehicle and an opposing-through vehicle, data regarding paths 18 taken by permissive left-turn vehicles through the intersection is collected, and the extents 18a, 18b, i.e., the outermost paths of those for which data was collected, are identified, optionally ignoring outliers. In addition, data regarding paths 20 taken by opposing-through vehicles through the intersection is collected, and the extents 20a, 20b are identified, optionally ignoring outliers. A conflict zone 16 of the class-pair is defined in the area bounded by the extents 18a, 18b of the paths taken by permissive left-turn vehicles and the extents 20a, 20b of the paths taken by opposing-through vehicles during the predetermined time period.

[0060] According to some examples, the traffic control system 10 may be configured to determine conflict zones in the intersection for a class-pair at different times, for example at peak usage times on weekdays, late night on weekends, etc.

[0061] As explained in more detail below, the conflict zone 16 may be expanded to comprise a crashclearance region, for example to allow for traffic conflicts to be detected even if two road users are predicted to be in a conflict zone within an amount of time below a predetermined threshold.

[0062] According to some examples, the crash-clearance region is based on atime-to-collision (TTC) approach, and is determined such that a first of the identified road users leaves the conflict zone a predetermined amount of time before a second of the identified road users, being a vehicle, reaches the conflict zone without considering deceleration of the second road user.

[0063] According to some examples, the crash-clearance region is based on a post-encroachment- time (PET) approach, and is determined such that a first of the identified road users leaves the conflict zone a predetermined amount of time before a second of the identified road users, being a vehicle, reaches the conflict zone considering deceleration of the second road user.

[0064] As mentioned above, a potential traffic conflict is detected if two road users are predicted to be in a conflict zone at the same time. The traffic control system 10 is configured to apply a suitable method for each class-pair in making this detection.

[0065] While crash-clearance regions are considered expansions of the conflict zone, they may be expressed as modifications of systems for detecting traffic conflicts, without altering the conflict zones directly.Permissive Right-Turn Vehicle (RTV) and Vulnerable Road User (VRU)

[0066] In general, it is expected that when the trajectory of a permissive right-turn vehicle traverses that of a vulnerable road user, as illustrated in Fig. 4A, the permissive right-turn vehicle should yield, and if it doesn't, e.g., entering the intersection by crossing the stop line, then a potential traffic conflict may be detected if the permissive right-turn vehicle is predicted to reach the conflict zone 16, i.e., if the driver is not expected to be able to stop in time. Accordingly, a predicted stopping distance d of the rightturn vehicle exceeds and a minimum allowable stopping distance dmmare calculated, and a potential traffic conflict is detected if d > dmin.

[0067] The predicted stopping distance d may be given by:where VR is the speed in m / s of the permissive right-turn vehicle as it passes a stop line entering the intersection, to is a perception-reaction time in seconds, (p is a maximum deceleration rate in m / s2, g is the gravitational acceleration rate in m / s2, and G is the road grade percentage (positive for an uphill grade and negative for a downhill grade). When speed is expressed in ft / s and acceleration / deceleration rates are expressed in ft / s2, the coefficients 0.278 and 254 should be replaced, respectively, with 1.47 and 30.

[0068] The minimum allowable stopping distance dminmay be given by:where d\ is the distance from the curb to the centerline of the lane in which the permissive right-turn vehicle approaches the intersection, and tfe is the distance from the curb to the centerline of the lane closest to the curb which the vulnerable road user is crossing, and if d > dmin, then the RT vehicle will not stop out of the conflict area and will generate a traffic conflict.Permissive Left-Turn Vehicle (LTV) and Opposing-Through Vehicle (OTV)

[0069] A permissive left-turn vehicle runs into a conflict w ith opposing through vehicles when its front end enters the opposing through lanes until its rear end leaves that area. During this hazardous period, the permissive LT vehicle’s total (linearized) travel distance D and travel time t can be roughly estimated as: d=8(L+N w) t = d / vQ(3) where L is a vehicle’s length; N is the number of lanes; w is the lane width; 5 is an empirical factor to consider the LT vehicle’s curvy movement and curb spaces; and vo is the LT vehicle’s instantaneous speed.

[0070] Whenever a permissive LT vehicle starts to turn, it means that the driver has perceived an acceptable gap and decided on a safe crossing speed. It is also reasonable to assume that the permissive LT vehicle has no chance to change its decision while turning due to the impact of centrifugal force and a limited vision, etc. As such, if the permissive LT vehicle’s maneuver is unsafe, then avoiding a crash will mostly rely on the evasive responses by the opposing through vehicles, such as slowing down to keep a minimal safe clearance from the LT vehicles. The safe clearance is the time difference when two conflicting conflict vehicles enter the conflict zone (see Fig. 5). It plays a similar role with the postencroachment time (PET) except it is considered a conflict zone instead of a conflict point. Without confusion, the term PET will be used to describe this safety clearance.

[0071] When a permissive left-turn vehicle crosses in front of an opposing-through vehicle, as illustrated in Fig. 4B, there is a possibility for a traffic conflict while the left-turn vehicle is at least partially in the path of the opposing-through vehicle. A potential traffic conflict may be detected between a permissive left-turn vehicle and opposing-through vehicle if the opposing-through vehicle is predicted to reach the conflict zone 16 while the permissive left-turn vehicle is predicted to be at least partially within the conflict zone.

[0072] Once the permissive left-turn vehicle enters the conflict zone 16, it is assumed that its speed will remain constant, i.e., the driver of the permissive left-turn vehicle will not adjust their speed whiletraversing the conflict zone. Accordingly, the time from when the permissive left-turn vehicle enters the conflict zone 16 until the opposing-through vehicle reaches it is assumed to be dependent entirely on the reaction of the driver of the opposing-through vehicle.

[0073] The predicted travel distance of the opposing-through vehicle from when the permissive left-turn vehicle enters the conflict zone 16 until the permissive left-turn vehicle entirely exits the conflict zone may be given by:where vo is the initial speed in m / s of the opposing-through vehicle, to is a perception-reaction time in seconds, is the time in seconds during which any part of the permissive left-turn vehicle is predicted to be within the conflict zone, (p is a maximum deceleration rate in m / s2, g is the gravitational acceleration rate in m / s2, and G is the road grade percentage (positive for an uphill grade and negative for a downhill grade). When speed is expressed in ft / s and acceleration / deceleration rates are expressed in ft / s2, the coefficients 0.278 and 254 should be replaced, respectively, with 1.47 and 30. A value for fc may be given by:where d is an empirical factor which takes into account a predicted curved trajectory of the permissive left-turn vehicle and intersection geometry, L is a vehicle length associated with the permissive left-turn vehicle, w is the total width of all opposing traffic lanes which the permissive left-turn vehicle crosses during its turn, and VL is the speed of the permissive left-turn vehicle. The value for L may be the actual length of the permissive left-turn vehicle, for example measured by the tracking system 14, based on a known length of the vehicle (e.g., wherein the traffic control system 10 is configured to identify the model of a vehicle), etc., or it may be an estimated value.

[0074] If the permissive left-turn vehicle enters the conflict zone 16 when the distance of the opposing- through vehicle to the conflict zone is less than the predicted travel distance for example as given above, a potential traffic conflict is detected.

[0075] Thus, assuming the through vehicle is willing to take the maximal or larger deceleration in this process, its (decelerating) travel distance d during t is at least: d = 0.278

[0076] Eq. (5) represents a boundary condition for the opposing through vehicle at an instantaneous speed v0. Once the LT vehicle enters the conflict zone, the through vehicle takes T seconds of P-R time and then slows down. If a deceleration larger than the maximum must be taken, then the throughvehicle will experience a traffic conflict. In other words, the opposing vehicle must be at least d feet away from the conflict zone when the permissive LT vehicles enter the conflict zone to avoid an evasive deceleration maneuver.Permissive Left-Turn Vehicle (LTV) and Vulnerable Road User (VRU)

[0077] In general, it is expected that when the trajectory’ of a permissive left-turn vehicle traverses that of a vulnerable road user, as illustrated in Fig. 4C, the permissive left-turn vehicle is assumed to brake late or not at all, for example to avoid a potential collision with an approaching opposing- through vehicle. Accordingly, if the permissive left-turn vehicle and the vulnerable road user are in the conflict zone 16 at the same time, a potential traffic conflict is detected. To afford extra protection to the vulnerable road user, the speed of the permissive left-turn vehicle is not considered.Permissive Right-Turn Vehicle (RTV) and U-Turn Vehicle (UTV)

[0078] Permissive RT vehicles and U-turn vehicles (during protected or permissive LT phases) can have a conflict due to the LT vehicle drivers’ negligence. Even though both vehicles may run slowly they may be dangerously close and cause evasive brakes. As illustrated in Fig. 4D, a potential traffic conflict may be detected between a permissive right-tum vehicle and U-tum vehicle if they are in the conflict zone 16 simultaneously.Red Light Running (RLR)

[0079] RLR is a special traffic conflict at signalized intersections, and a red-light runner is considered to have a “traffic conflict” with the yellow ends. In the US, most states take a “permissive yellow” law to define an RLR event, meaning that it is legal for a vehicle’s front bumper to cross the stop line any time before the yellow ends and take all-read clearance or even first few seconds of other green phases to clear the intersection. The driver’s decision causing an RLR is twofold: if the driver decides to cross, then it may misjudge the remaining yellow time; if the driver decides to stop, then it may be too close to stop. A red-light runner does not have a conflict with other moving vehicles and it should be measured directly.

[0080] The traffic control system 10 may be further configured to detect a potential traffic conflict when a single vehicle runs a red light. (This may be considered a special class-pair between a red light running vehicle and the traffic light.) As illustrated in Fig. 4E, the traffic control system is configured to determine a conflict zone 16 for the vehicle and a red light, identify an approaching vehicle, and detect a traffic conflict if the vehicle enters the red-light conflict zone when subject to a red light, i.e., runs the red light.

[0081] The severity of traffic conflicts may or may not be associated with conflicting objects’ speeds. For traffic conflicts involving slow VRUs or vehicles, the severity of traffic conflicts betweenvehicles and VRUs can be solely determined by their proximity. If the conflict zone is scoped small, then only those dangerously proximate traffic conflicts will be captured. With a larger conflict zone, more traffic conflicts will be captured including both severe and less severe traffic conflicts.

[0082] For high-speed, vehicle-to-vehicle traffic conflicts (e.g., permissive LT vehicles vs. opposing through vehicles), the traffic conflicts are evaluated by whether the vehicle(s) must take evasive actions to avoid collision. This criterion involves both proximity and speed. The severity of highspeed traffic conflicts is important to estimate the vehicle-to-vehicle crash risks. For instance, a “bumper-to-bumper” traffic conflict is more dangerous than that with seconds of PET. Given that state-of-the-art roadside sensors can only directly measure vehicle positions and speeds but need to derive accelerations, it makes sense to choose the time-to-collision (TTC) and Post-encroachment time (PET) to measure the traffic conflict severity. As shown in Fig. 1, TTC is the elapsed time from when the first conflicting vehicle leaves the conflict zone to when the second conflicting vehicle is projected to arrive at the conflict zone without deceleration. PET is the time gap between when the first conflicting vehicle leaves the conflict zone and when the second conflicting vehicle arrives at the conflict zone, with an attempt to avoid a collision by deceleration. Therefore, PET is always equal to or greater than TTC in the same scenario. TTC and PET are in essence the safety buffer between conflicting vehicles. The kinematic analysis of the situation depicted in Fig. 3 is a special case in which both TTC and PET are set to zero. In other words, if the kinematic analysis is used to scope the conflict zone, then any captured traffic conflicts will be of “bumper-to-bumper” types. Less severe traffic conflicts, however, hold the same interest because the highly dangerous traffic conflicts will be similarly rare as real crashes.

[0083] Let TTTCand TPETdenote the minimally acceptable safety clearance (i.e., minimal allowed proximity between conflict vehicles). Then conflict zones defined in Figure 4 can be extended to accommodate the TTC or PET. Once two fast conflicting vehicles appear in an expanded conflict zone at the same time, it means they are proximate enough to generate a traffic conflict. For the four conflict zones:• Conflict zones between the RT vehicles and VRUs: the RT vehicle is supposed to unconditionally yield to VRUs. Therefore, TTC and PET are not considered. Using smaller conflict zones will ensure focusing on the most dangerous traffic conflicts only. Using larger zones will reflect a strict protection rules for the VRUs.• Conflict zones between the permissive LT vehicles and concurrent pedestrians: since the permissive LT vehicles are unlikely to decelerate, the conflict zone can be expanded according to the TTC threshold as shown in Fig. 6. Assuming a concurrent VRU enters the intersection at the WALK onset, t0, and reaches the medium at ty, a traffic conflict can be identified if a permissiveLT vehicle and a pedestrian appear in the expanded conflict zone between t0and t15meaning they are dangerously proximate. Whenever a permissive LT vehicle enters the extended conflict zone with concurrent VRUs (the blue area) at t, the vehicle’s predicted arriving time to the crossing (the red area) will be predicted, t2. If t2is sooner than+ TTC, then a traffic conflict can be identified. Note that VRUs take much longer to clear the conflict zone. Therefore, it is almost certain that a near-miss can be identified whenever permissive LT vehicles and concurrent crossing pedestrians are identified at the same time within the extended conflict zone. The average length of the extended conflict zone can be jointly determined by the prevailing LT speed, intersection layouts, and target predicting time window (i.e., how many seconds in advance?).• Conflict zones between permissive LT vehicles and opposing through vehicles: Assuming that only the opposing through vehicles will decelerate, the conflict zone can be expanded according to PET from Eq. (6). As shown in Fig. 7, whenever a permissive LT vehicle v enters the conflict zone at t = t0and leaves at t = tq (calculated according to measured instantaneous vehicle speed, vehicle length, and projected lateral path). This vehicle blocks the through lanes for (t- + PET — t0) seconds. If an opposing vehicle v3is far enough (d2or farther) at t0, then it does not need to respond to the lane blockage. If an opposing vehicle is proximate, then it must decelerate to arrive at the conflict zone no earlier than t2to avoid a traffic conflict. The more proximate they are, the larger brake needs to be taken. When the opposing vehicle must take the nr maximal deceleration, 3.41 — recommended by AASHTO (28), then its instantaneous distance d is the minimal distance closer than which the opposing vehicle must take an evasive brake. An opposing through vehicle will experience a traffic conflict with the permissive LT vehicle if it is closer to the conflict zone than d at t.The shortest distance d can be calculated as Eq. (6). Where v0is the opposing through vehicle's instantaneous speed at t0, T is the perception-reaction or P-R time.Note that the P-R time may not apply because the through vehicle driver may have noticed the likely LT maneuvers even before lane blockage (See Eq. (7)). d > dr' and so we should aways adopt Eq. (6) to scope the conflict zones.• Red-light running: There are no associated TTC or PET for this special traffic conflict. So, the conflict zone is not expanded.• Conflict zones for permissive LT vehicles and U-turn vehicles: The traffic conflict will be caused by drivers’ negligence and vehicles are relatively slow. The traffic conflict can be solely determined by the proximity.EXAMPLESExample 1: Evaluating high-speed traffic conflicts at intersections

[0084] There is only one type of high-speed vehicle-to-vehicle traffic conflicts at intersections: permissive LT vehicles vs. opposing through vehicles. The conflict zone will be scoped as illustrated in Fig. 7, covering both the crash zone and the expanded area for PET. Given the target PET and prevailing approaching speed, the shortest distance from the crash zone, di, can be calculated with Eq. (6). Other conditions for identifying a high-speed traffic conflict include:• permissive LT vehicles should enter the conflict zone before the opposing through vehicle to ensure that the opposing through vehicle takes evasive brakes even though it has the right of way during the permissive left-turn phase.• the opposing through vehicle should be faster than the design speed in Eq. (6). Slow-approaching vehicles do not necessarily need to take hard brakes to avoid a crash.

[0085] During a permissive left-turn phase (e.g., Flashing Yellow Arrow), whenever an opposing through vehicle enters the conflict zone at t (t0< t < t2), d, feel away from the crash zones, it will check the following conditions (illustrated in Fig. 7):1. Whether this vehicle faster (tq) than the designed approaching speed (v0).2. Whether a blocking permissive LT vehicle which enters the conflict zone earlier at t0and block the through lanes until t2(considering its lane-occupying time plus PET).

[0086] If the above two conditions are met and the through vehicle is railing to keep taking amax— TL—3.41 — deceleration until it arrives at the crash zone at tx, then txcan be calculated as:

[0087] If the P-R time T is large, then it will be possible that the subj ect vehicle will keep moving atuntil it reaches the crash zone at tx— t + — .

[0088] If tx< t2(e.g., the through vehicle is fast), then two vehicles rail either crash or generate a traffic conflict. By selecting various target PET values, we can selectively capture the traffic conflicts according to the level of severity.In this case,Example 2: Instantaneous near-miss identification using LiDAR

[0089] LiDAR is short for Light Detection and Range and is an emerging technology to track moving objects. The LiDAR sensors have been tested and proven effective for both vehicles and VRUs detection and tracking at intersections (29). In this case study, a LiDAR tracking solution was deployed at a signalized intersection in Salt Lake City, Utah (See Fig. 8). The LiDAR tracking is also synchronized with traffic signal states. This case study focused on the high-speed permissive LT vehicles vs opposing through vehicles during the permissive LT phase because it is relatively complex compared with other types of traffic conflicts solely defined by objects’ proximity.

[0090] The LiDAR sensors can track each vehicle’s instantaneous speed and length in real-time. During the permissive NB left-turn phases, whenever an SB vehicle enters one of the conflict zones (e.g., Zone 77), the algorithm will check if this zone is being occupied by a permissive LT vehicle and estimate its remaining time t2(considering the PET) according to the LT vehicle's speed and length. Then the SB vehicle’s arriving time at the crash zone will be estimated with Eq. (8). If the SB vehicle’s arriving time txis earlier than the NB LT vehicle’s clearance time t2. then a traffic conflict will be reported. The corresponding TTC and PET are calculated with Eq. (9).

[0091] The extended conflict zones were scoped according to Eq. (6). The SB prevalent speed entering the near-miss zone was around 48 km / h which was used to scope the near-miss zones. The left-turn vehicle’s speed was set to 16 km / h and each vehicle length was reported by the LiDAR sensor; PET=2.0 s,’ max deceleration rate is -3.41 — s2’ P-R time is set to 1.5 s.

[0092] During the 4 hours of the experiment, the LiDAR-based algorithm reported all the traffic conflicts (permissive NB LT vehicles vs. opposing SB vehicles). Fig. 9 shows atable showing the format of instantaneously reported traffic conflicts.

[0093] At the same time, a camera installed at that intersection was used to record the live traffic (See Fig. 8). The algorithm reported 38 instantaneous traffic conflicts within 4 hours. Both LiDAR-reported traffic conflicts and the live traffic were monitored to determine if a LiDAR-reported traffic conflict is valid. All the LiDAR-reported traffic conflicts w ere validated. Later, the recorded video w as reviewed again and then manually measured the PET from the footprint and compared it with the LiDAR-reported PET values (see Fig. 10). They were highly correlated. Importantly, not all 38 records could be further evaluated because some frames in the footprint were lost while being recorded.

[0094] It was noticed that the LiDAR-reported PETs were not the same as the ground truth. There are several reasons. First, the PET was calculated according to Eq. (8) and Eq. (9) assuming a perception-reaction time for the through vehicle, the subject vehicle may have recognized the imminent crash risk and already decelerated when entering the conflict zone, causing the longer PETor even false alarm (through vehicle driver can take a lighter brake to avoid collisions). Second, some SB vehicles were much faster than the designed speed 48 km / h or entered the conflict zone a few seconds after the permissive LT vehicle began to turn. This caused a small PET. Nonetheless, the reporting accuracy is overall accurate and acceptable.

[0095] In the present disclosure, a fast method to capture instantaneous traffic conflicts is presented. Compared to the existing trajectory -based near-miss identifying algorithms, this system is based on the conflicting vehicles’ instantaneous speeds and proximity. Whenever conflicting moving vehicles are dangerously proximate, a traffic conflict can be identified. Instead of continuously processing many trajectories to identify traffic conflicts, the proposed system only needs to check if conflict vehicles appear in the pre-scoped conflict zone at the same time. The proximity-based method can significantly reduce the computing load to identify traffic conflicts and therefore this task can be achieved in real time.

[0096] For the traffic conflicts involving slow VRUs or slow vehicles, the traffic conflicts can be identified solely based on the proximity. For high-speed, vehicle-to-vehicle traffic conflicts at intersections (permissive LT vehicles vs. opposing through vehicles), both proximity and speed need to be considered according to the kinematic equations.

[0097] In the case study, the proximity-based near-miss identification algorithm is implemented with state-of-the-art LiDAR sensing technologies and associated with traffic signal systems. From the experiment carried out in Salt Lake City, Utah, the instantaneous traffic conflicts captured by the LiDAR sensors were slightly different from the ground truth, but they were all validated, and the difference was acceptable.

[0098] Accurate near-miss identification in real-time will pave the road for dynamic safety-centric traffic control strategies at intersections in the future. The cunent trajectory -based systems require lots of computing resources and can hardly be real-time. As such, the existing systems are more suitable for post-analysis to reveal the traffic safety issues. In contrast, real-time near-miss identification is expected to become a new foundational input for traffic signal systems, like vehicle actuations in various traffic control strategies.

[0099] It will be recognized that examples, embodiments, modifications, options, etc., described herein are to be construed as inclusive and non-limiting, i.e., two or more examples, etc., described separately herein are not to be construed as being mutually exclusive of one another or in any other way limiting, unless such is explicitly stated and / or is otherwise clear. Those skilled in the art to which this invention pertains will readily appreciate that numerous changes, variations, and modifications can be made without departing from the scope of the presently disclosed subject matter, mutatis mutandis.

Claims

CLAIMS:

1. A traffic control system configured for being operatively coupled to a traffic signal system, the traffic control system comprising:• a tracking system, comprising one or more tracking sensors configured to identify road users associated with an intersection, and to measure the speeds and locations of identified road users; and• a controller, configured to: o identify two road users associated with the intersection, and measure their instantaneous locations and speeds; o assign the identified road users to a predefined class-pair, the class-pair comprising a classification indicating a type and / or trajectory through the intersection of each of the identified road users; o determine a conflict zone within the intersection for the assigned class-pair; o predict, based on instantaneous measurements by the tracking system of the two identified road users, when each will be within the conflict zone; and o detect a potential traffic conflict when the two identified road users are predicted to be within the conflict zone simultaneously.

2. The traffic control system according to claim 1, wherein the controller is further configured to operate the traffic signal system to mitigate the risk of traffic conflicts within the intersection between pairs of road users matching the classifications of the two identified road users.

3. The traffic control system according to any one of the preceding claims, wherein determining the conflict zone within the intersection for the determined class-pair comprises:• for each classification of the class-pair, assessing the extents of the expected trajectories of road users within the intersection; wherein the conflict zone comprises a base region of the intersection bounded by the extents of the expected trajectories of the class-pair.

4. The traffic control system according to claim 3, wherein assessing the extents of the expected trajectories comprises monitoring the intersection for a predetermined amount of time and storing trajectory information of road users.

5. The traffic control system according to any one of claims 3 and 4, wherein the conflict zone further comprises a crash-clearance region, the crash-clearance region being determined suchthat a first of the identified road users leaves the conflict zone a predetermined amount of time before a second of the identified road users, being a vehicle, reaches the conflict zone without decelerating.

6. The traffic control system according to any one of claims 3 and 4, wherein the conflict zone further comprises a crash-clearance region, the crash-clearance region being determined such that a first of the identified road users leaves the conflict zone a predetermined amount of time before a second of the identified road users, being a vehicle, reaches the conflict zone with decelerating.

7. The traffic control system according to any one of the preceding claims, wherein the identified road users are assigned to a class-pair comprising a permissive right-turn vehicle and a vulnerable road user.

8. The traffic control system according to claim 7, wherein a potential traffic conflict is detected if the permissive right-tum vehicle is predicted to reach the conflict zone if a predicted stopping distance thereof exceeds a minimum allowable stopping distance.

9. The traffic control system according to claim 8, wherein the predicted stopping distance is given by:where VR is the speed in m / s of the permissive right-tum vehicle as it passes a stop line entering the intersection, to is a perception-reaction time in seconds, tp is a maximum deceleration rate in m / s2, g is the gravitational acceleration rate in m / s2, and G is the road grade percentage.

10. The traffic control system according to any one of claims 8 and 9, wherein the shortest allowable stopping distance is given by:MP ®2, where d\ is the distance from the curb to the centerline of the lane in which the permissive right-tum vehicle approaches the intersection, and c / 2 is the distance from the curb to the centerline of the lane closest to the curb which the vulnerable road user is crossing.

11. The traffic control system according to any one of the preceding claims, wherein the identified road users are assigned to a class-pair comprising a permissive left-turn vehicle and an opposing-through vehicle.

12. The traffic control system according to claim 11 , wherein a potential traffic conflict is detected if the opposing-through vehicle is predicted to reach the conflict zone while the permissive left-turn vehicle is predicted to be at least partially within the conflict zone.

13. The traffic control system according to claim 12, wherein the predicted travel distance of the opposing-through vehicle while the permissive left-turn vehicle is at least partially within the conflict zone is given by:where vo is the initial speed in m / s of the opposing-through vehicle, to is a perception-reaction time in seconds, fc is the time in seconds during which any part of the permissive left-turn vehicle is predicted to be within the conflict zone, (p is a maximum deceleration rate in m / s2, g is the gravitational acceleration rate in m / s2, and G is the road grade percentage.

14. The traffic control system according to claim 13, wherein the amount of time fc during which any part of the permissive left-turn vehicle is predicted to be within the conflict zone is given by:S(L+w) where S is an empirical factor which takes into account a predicted curved trajectory of the permissive left-turn vehicle and intersection geometry, L is a vehicle length associated with the permissive left-turn vehicle, w is the total width of all opposing traffic lanes which the permissive left-turn vehicle crosses during its turn, and VL is the speed of the permissive leftturn vehicle.

15. The traffic control system according to any one of the preceding claims, wherein the identified road users are assigned to a class-pair comprising a permissive left-turn vehicle and a vulnerable road user.

16. The traffic control system according to claim 15, wherein a potential traffic conflict is detected if the permissive left-turn vehicle and the vulnerable road user are predicted to be in the conflict zone simultaneously.

17. The traffic control system according to any one of the preceding claims, wherein the identified road users are assigned to a class-pair comprising a permissive right-turn vehicle and a U-turn vehicle.

18. The traffic control system according to claim 17. wherein a potential traffic conflict is detected if the permissive right-turn vehicle and U-tum vehicle are predicted to be in the conflict zone simultaneously.

19. The traffic control system according to any one of the preceding claims, being further configured to:• identify a road user approaching a signalized intersection and measure its instantaneous location and speed;• determine a red-light conflict zone within the intersection; and• detect a potential traffic conflict if the road user enters the red-light conflict zone when subj ect to a red-light traffic signal indicator.

20. The traffic control system according to any one of the preceding claims, wherein the tracking sensors comprise Light Detection and Ranging (LiDAR) sensors or any other comparable tracking sensor.

Images