MULTIPLE INTERSECTIONS OF SPACE-TIME ANISOTROPIC GAUSSIAN FIELDS

Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian field with indices H=(H_(1),…,H_(N))∈(0,1)~N,where the components X_(i)(i=1,…,d)of X are independent,and the canonical metric√(E(X_(i)(t)-X_(i)(s))^(2))^(1/2)(i=1,…,d)is commensurate with■for s=(s_(1),…,s_(N)),t=(t_(1),…,t_(N))∈R~N,α_(i)∈(0,1],and with the continuous functionγ(·)satisfying certain conditions.First,the upper and lower bounds of the hitting probabilities of X can be derived from the corresponding generalized Hausdorff measure and capacity,which are based on the kernel functions depending explicitly onγ(·).Furthermore,the multiple intersections of the sample paths of two independent centered space-time anisotropic Gaussian fields with different distributions are considered.Our results extend the corresponding results for anisotropic Gaussian fields to a large class of space-time anisotropic Gaussian fields.

Experimental and numerical investigation of droplet flow mechanisms at fracture intersections

Understanding unsaturated flow behaviors in fractured rocks is essential for various applications.A fundamental process in this regard is flow splitting at fracture intersections.However,the impact of geometrical properties of fracture intersections on flow splitting is still unclear.This work investigates the combined influence of geometry(intersection angle,fracture apertures,and inclination angle),liquid droplet length,inertia,and dynamic wetting properties on liquid splitting dynamics at fracture intersections.A theoretical model of liquid splitting is developed,considering the factors mentioned above,and numerically solved to predict the flow splitting behavior.The model is validated against carefullycontrolled visualized experiments.Our results reveal two distinct splitting behaviors,separated by a critical droplet length.These behaviors shift from a monotonic to a non-monotonic trend with decreasing inclination angle.A comprehensive analysis further clarifies the impacts of the key factors on the splitting ratio,which is defined as the percentage of liquid volume entering the branch fracture.The splitting ratio decreases with increasing inclination angle,indicating a decrease in the gravitational effect on the branch fracture,which is directly proportional to the intersection angle.A non-monotonic relationship exists between the splitting ratio and the aperture ratio of the branch fracture to the main fracture.The results show that as the intersection angle decreases,the splitting ratio increases.Additionally,the influence of dynamic contact angles decreases with increasing intersection angle.These findings enhance our understanding of the impact of geometry on flow dynamics at fracture intersections.The proposed model provides a foundation for simulating and predicting unsaturated flow in complex fractured networks.

Analysis of Stopping Behavior at Rural T-Intersections Using Naturalistic Driving Study Data

Rural intersections account for around 30% of crashes in rural areas and 6% of all fatal crashes, representing a significant but poorly understood safety problem. Crashes at rural intersections are also problematic since high speeds on intersection approaches are present which can exacerbate the impact of a crash. Additionally, rural areas are often underserved with EMS services which can further contribute to negative crash outcomes. This paper describes an analysis of driver stopping behavior at rural T-intersections using the SHRP 2 Naturalistic Driving Study data. Type of stop was used as a safety surrogate measure using full/rolling stops compared to non-stops. Time series traces were obtained for 157 drivers at 87 unique intersections resulting in 1277 samples at the stop controlled approach for T-intersections. Roadway (i.e. number of lanes, presence of skew, speed limit, presence of stop bar or other traffic control devices), driver (age, gender, speeding), and environmental characteristics (time of day, presence of rain) were reduced and included as independent variables. Results of a logistic regression model indicated drivers were less likely to stop during the nighttime. However presence of intersection lighting increased the likelihood of full/rolling stops. Presence of intersection skew was shown to negatively impact stopping behavior. Additionally drivers who were traveling over the posted speed limit upstream of the intersection approach were less likely to stop at the approach stop sign.

Characteristics and risk of violation behavior of non-motorists at signalized intersections

Aiming at prevalent violations of non-motorists at urban intersections in China, this paper intends to clarify the characteristics and risks of non-motorist violations at signalized intersections through questionnaires and video recordings, which may serve as a basis for non-motorized vehicle management. It can help improve the traffic order and enhance the degree of safety at signalized intersections. To obtain the perception information, a questionaire survey on the Internet was conducted and 972 valid questionnaires were returned. It is found that academic degree contributes little to non-motorist violations, while electrical bicyclists have a relatively higher frequency of violations compared with bicyclists. The video data of 18 228 non-motorist behaviors indicate that the violation rate of all non-motorists is 26.5%; the number of conflicts reaches 1 938, among which violation conflicts account for 66.8%. The study shows that the violation rates and the violation behavior at three types of surveyed intersections are markedly different. It is also concluded that the conflict rates and the violation rates are positively correlated. Furthermore, signal violation, traveling in the wrong direction, and overspeeding to cross the intersection are the most dangerous among traffic violation behaviors.

Method for pedestrian signal timing at signalized intersections

The pedestrian timing at signalized intersections is studied aiming at the problems of the inconsistency of the vehicular and pedestrian timing requirements and the insufficiency of pedestrian clearance. Based on the formulae of WALK and flashing DON＇T WALK （FDW） in the highway capacity manual （HCM）, the relationship between pedestrian signal indications and vehicular signal indications is discussed using the theory of traffic flow. Then, methods of pedestrian timing for different cases are established, particularly the methods of the pedestrian green adjustment. Ways of pedestrian crossing are analyzed for roadways with different forms and widths of the median island. The sampling values of calculation parameters are studied, and the recommended formulae of pedestrian timing for different conditions are presented.

Analysis on intersections between fractures by parallel computation

The discrete fracture network model is a powerful tool for fractured rock mass fluid flow simulations and supports safety assessments of coal mine hazards such as water inrush.Intersection analysis,which identifies all pairs of intersected fractures(the basic components composing the connectivity of a network),is one of its crucial procedures.This paper attempts to improve intersection analysis through parallel computing.Considering a seamless interfacing with other procedures in modeling,two algorithms are designed and presented,of which one is a completely independent parallel procedure with some redundant computations and the other is an optimized version with reduced redundancy.A numerical study indicates that both of the algorithms are practical and can significantly improve the computational performance of intersection analysis for large-scale simulations.Moreover,the preferred application conditions for the two algorithms are also discussed.

Adaptive neuro-fuzzy interface system for gap acceptance behavior of right-turning vehicles at partially controlled T-intersections

Gap acceptance theory is broadly used for evaluating unsignalized intersections in developed coun tries. Intersections with no specific priority to any move ment, known as uncontrolled intersections, are common in India. Limited priority is observed at a few intersections, where priorities are perceived by drivers based on geom etry, traffic volume, and speed on the approaches of intersection. Analyzing such intersections is complex because the overall traffic behavior is the result of drivers, vehicles, and traffic flow characteristics. Fuzzy theory has been widely used to analyze similar situations. This paper describes the application of adaptive neurofuzzy interface system （ANFIS） to the modeling of gap acceptance behavior of rightturning vehicles at limited priority Tintersections （in India, vehicles are driven on the left side of a road）. Field data are collected using video cameras at four Tintersections having limited priority. The data extracted include gap/lag, subject vehicle type, conflicting vehicle type, and driver＇s decision （accepted/rejected）. ANFIS models are developed by using 80 % of the extracted data （total data observations for major road right turning vehicles are 722 and 1,066 for minor road right turning vehicles） and remaining are used for model vali dation. Four different combinations of input variables are considered for major and minor road right turnings sepa rately. Correct prediction by ANFIS models ranges from 75.17 % to 82.16 % for major road right turning and 87.20 % to 88.62 % for minor road right turning. Themodels developed in this paper can be used in the dynamic estimation of gap acceptance in traffic simulation models.

Ultrafast Dynamics Through Conical Intersections in 2,6-dimethylpyridine Studied with Time-resolved Photoelectron Imaging

The ultrafast dynamics through conical intersections in 2,6-dimethylpyridine has been studied by femtosecond time-resolved photoelectron imaging coupled with time-resolved mass spectroscopy. Upon absorption of 266 nm pump laser, 2,6-dimethylpyridine is excited to the S2 state with a ππ character from So state. The time evolution of the parent ion signals consists of two exponential decays. One is a fast component on a timescale of 635 fs and the other is a slow component with a timescale of 4.37 ps. Time-dependent photo- electron angular distributions and energy-resolved photoelectron spectroscopy are extracted from time-resolved photoelectron imaging and provide the evolutive information of S2 state. In brief, the ultrafast component is a population transfer from S2 to S1 through the S2/S1 conical intersections, the slow component is attributed to simultaneous IC from the S2 state and the higher vibrational levels of S1 state to So state, which involves the coupling of S2/S0 and S1/So conical intersections. Additionally, the observed ultrafast S2--＋S1 transition occurs only with an 18% branching ratio.

Study on Geometric Factors Influencing Saturation Flow Rate at Signalized Intersections under Heterogeneous Traffic Conditions

The main objective of intersection design is to facilitate the convenience, comfort, and safety of people traversing the intersection by enhancing the efficient movement of road users. The intersections on urban roads in India generally cater to heterogeneous motorized traffic, along with slow-moving traffic including pedestrians. It is therefore necessary to consider saturation flow for mixed traffic conditions to evaluate the overall operation of signalized intersections. A proper traffic model must consider varying characteristics of all the road users to effectively design and efficiently manage signalized intersections. This paper presents the results of the study on analyses of saturation flow rate conducted at signalized intersections with mixed traffic conditions in the city of Bangalore, India. Studies were carried out at 15 signalized intersections in the city of Bangalore with varying geometric factors such as width of road (w), gradient of the road (g), and turning radius (r) for right turning vehicles. Saturation flow rate computed as per Highway Capacity manual (HCM: 2000), Indonesian highway capacity manual (IHCM), and IRC SP: 41-1994 was compared with the field observations. The geometric factors, which affect the saturation flow, have been considered in this study and accordingly a new model has been proposed for determining saturation flow. It has been shown that by the introduction of the suggested adjustment factors in this paper, the saturation flow rate can give better picture of the field conditions, especially under heterogeneous traffic conditions of an urban area.

Multi-phase bus signal priority strategy at isolated intersections

To satisfy the multiple priority requests from buses that arrive at different phases within a small time window, a multi-phase bus signal priority （MPBSP） strategy is developed. The proximity principle is brought forward to settle the conflicts among multiple priority requests and arrange the optimal priority sequence. To avoid over saturation of the intersection, a conditional MPBSP algorithm that adopts early green and green extension strategies is developed to give priority to the bus with the highest priority level when green time that each phase runs makes its saturation degree not larger than 0. 95. Finally, the algorithm is tested in the VISSIM environment and compared with the normal signal timing algorithm. Sensitive analysis of the number of priority phases, bus demand, and volume to capacity ratios are conducted to quantify their impacts on the benefits of the MPBSP. Results show that the MPBSP strategy can effectively reduce bus delays, and with the increase in the number of priority phases, the reduction range of bus delays also increases.

Analytical method of minimum spacing of signalized intersections on bidirectional two-lane highways

In order to improve the smoothness of traffic flow on bidirectional two-lane highways, an analytical method is proposed to optimize the minimum spacing of the signalized intersections. The minimum signal spacing is determined by two parts, including the necessary distance for stabilizing the traffic flow after it passes through the signalized intersections and the length of the upstream functional area of intersection. For the former, based on the platoon dispersion theory, the stable distance determination problem of traffic flow is studied and a model of dispersion degrees varying with the distance from the upstream intersection is presented, in which the time headway is intended to yield the shifted negative exponential distribution. The parameters of the model for medal and collector highways are estimated respectively based on the field data. Then, the section at which the slope of dispersion degree curve equals -0.1 is regarded as the beginning of the dispersion stable state. The length of the intersection upstream functional area is determined by three parts, including the distance traveled during perception-reaction time, the distance traveled while a driver decelerates to a stop, and the queue storage length. Based on the above procedures, the minimum signal spacing of each highway category is proposed.

Decision-Making Models Based on Meta-Reinforcement Learning for Intelligent Vehicles at Urban Intersections

Behavioral decision-making at urban intersections is one of the primary difficulties currently impeding the development of intelligent vehicle technology.The problem is that existing decision-making algorithms cannot effectively deal with complex random scenarios at urban intersections.To deal with this,a deep deterministic policy gradient(DDPG)decision-making algorithm(T-DDPG)based on a time-series Markov decision process(T-MDP)was developed,where the state was extended to collect observations from several consecutive frames.Experiments found that T-DDPG performed better in terms of convergence and generalizability in complex intersection scenarios than a traditional DDPG algorithm.Furthermore,model-agnostic meta-learning(MAML)was incorporated into the T-DDPG algorithm to improve the training method,leading to a decision algorithm(T-MAML-DDPG)based on a secondary gradient.Simulation experiments of intersection scenarios were carried out on the Gym-Carla platform to verify and compare the decision models.The results showed that T-MAML-DDPG was able to easily deal with the random states of complex intersection scenarios,which could improve traffic safety and efficiency.The above decision-making models based on meta-reinforcement learning are significant for enhancing the decision-making ability of intelligent vehicles at urban intersections.

Coordinated Control of Traffic Signals for Multiple Intersections

The proper phase difference of traffic signals for adjacent intersections could decrease the time of operational delay. Some theorems show how to minimize the total average delay time for vehicle operating at adjacent intersections under given conditions. If the distance and signal cycles of adjacent intersections satisfy with specific conditions, the total average delay time would achieve zero. If the signal cycles of adjacent intersections and the phase difference of them are co-prime numbers, the total average delay time would be a constant. In general, if signal cycles of adjacent intersections and the phase difference of them are reducible numbers, the minimum total average delay time would be solved by the given algorithm. Numerical experiments have verified the rationality of these theorems.

THE MAXIMUM NUMBER OF INTERSECTIONS BETWEEN TWO PLANE RECTANGULAR PATHS

We show that the maximum number of intersections between two plane rectangular paths with lengths m and(mod 3); and it is mn+1 otherwise.

Experimental and numerical investigation of groundwater head losses on and nearby short intersections between disc-shaped fractures

Discrete fracture models are used for investigating precise processes of groundwater flow in fractured rocks,while a disc-shaped parallel-plates model for a single fracture is more reasonable and efficient for computational treatments.The flow velocity has a large spatial differentiation which is more likely to produce non-linear flow and additional head losses on and nearby intersections in such shaped fractures,therefore it is necessary to understand and quantify them.In this study,both laboratory experiments and numerical simulations were performed to investigate the total head loss on and nearby the intersections as well as the local head loss exactly on the intersections,which were not usually paid sufficient attention or even ignored.The investigation results show that these two losses account for 29.17%-84.97%and 0-73.57%of the entire total head loss in a fracture,respectively.As a result,they should be necessarily considered for groundwater modeling in fractured rocks.Furthermore,both head losses become larger when aperture and flow rate increase and intersection length decreases.Particularly,the ratios of these two head losses to the entire total head loss in a fracture could be well statistically explained by power regression equations with variables of aperture,intersection length,and flow rates,both of which achieved high coefficients of determination.It could be feasible through this type of study to provide a way on how to adjust the groundwater head from those obtained by numerical simulations based on the traditional linear flow model.Finally,it is practicable and effective to implement the investigation approach combining laboratory experiments with numerical simulations for quantifying the head losses on and nearby the intersections between disc-shaped fractures.

Human Factors in the Analysis of the ＂Tram-Car Drivers＂ at Intersections

The modem tramway has resurfaced as the cure to today＇s urban transport problems such as pollution, road congestion and uneven access to transit. However, trams at intersections often experience frequent and extended delays due to vehicles crossing the tram tracks. There is an increased potential for conflict between trams and vehicles at these locations and crashes are common. The question of the effects of human factors on trams crossroads safety has been little dealt with in literature. The general aim of this article is to further knowledge about the influence of tramway and surrounding environment on car＇s driver behavior at intersections. Understanding these influences, involve conducting a systematic review of the cognitive tasks related to driving and identifying the hazards that can arise at each task, and what factors can make these more or less likely to arise, considering the environmental design at intersections and behavioral factors. To achieve that, the HAZOP （Hazard and Operability Study） approach is conducted for this study. Concerning data collection, the methodology includes site visits to record user behavior and questionnaires to determine the opinion, concerns and knowledge of car drivers in interaction with the tram environment.

Safety Analysis for Older Drivers at SignalizedIntersections

The proportions of older drivers continue to increase since baby boom generation is becoming old. The level of mobility of older drivers is also increasing. Older drivers begin to noticeably be over-involved in fatal crashes. Intersections appear to be hazardous to older drivers, particularly left turn due to one or more of. sensory, perceptual, cognitive, physical and general driving knowledge deficiencies. The safety concern of older drivers is also becoming significant. Ten years of crash data has been extracted from Kansas accident report system. It has been analyzed using SAS （statistical analysis system） software. Five different age groups have been considered. Comparison has been made between different age groups of the same gender, and the same age group for different gender. Effects of light condition, weather condition, surface type, surface condition, road character and construction/maintenance zone on older drivers＇ safety have also been considered in this study. It has been found out that proportion of older drivers in through movement involved in accident decreases as age increases whereas the proportion of left turn accidents increases with age, left turn is harder for females in all age groups, and proportion of right turn accidents has no specific trend. Most of the accidents have taken place during daylight when there are no adverse weather conditions on dry surface, straight and level road, and blacktop surface type.

Model of Traffic Speed-Flow Relationship at Signal Intersections

Speed-flow relationship is the fundamental for the traffic simulation and traffic volume forecast. Traditional quadratic polynomial model can’t reflect the saturate flow at signal intersections. In order to determine the speed-flow relationship at signal intersections, the speed and time-headway of vehicles at two signal intersections were investigated and the accuracy of software used to get the speed was tested. After vehicle starting-up from queuing, the time-headway reduces gradually with the increase of speed. The relationship of power exponential function between speed and time-headway is formulated. Traffic volume can be calculated by the vehicle time-headway. Then the speed-flow relationship was developed and an S-shaped curve model was built in this paper. In the S-shaped curve model, traffic flow approaches to the saturate when the speed doesn’t increase. Thus, S-shaped curve model is better to describe the speed-flow relationship at signal intersection. The results can provide a reference to determine the parameters in traffic simulation and for the study of level of service of intersections.

Examining the Risk Factors of Rear-End Crashes at Signalized Intersections

Rear-end crashes are among the most common crash types at signalized intersections. To examine the risk factors for the occurrence of this crash type, this study involved the analysis of nine years of intersection crash records in the state of Wyoming. With that, the contributing factors related to crash, driver, environmental, and roadway characteristics, including pavement surface friction, were investigated. A binomial logistic regression modeling approach was applied to achieve the study’s objective. The results showed that three factors related to crash and driver’s attributes (commercial vehicle involvement, speeding, and driver’s age) and four factors related to environmental and roadway characteristics (lighting, weather conditions, area type, whether urban or rural and pavement friction) are associated with the risk of rear-end crash occurrence at signalized intersections. This study provides insights into the mitigation measures to implement concerning rear-end crashes at signalized intersections.

The Study of Fuzzy Line Control for Multiple Intersections

The line control for multiple intersections is a hot spot in the area of transportation. According to the principle of system analysis and coordination, a method about fuzzy line control for multiple intersections is proposed. The system is made of two control units, one is the basic control unit for every single intersection, and the other is used for the function of coordination.