WO2020248197A1

WO2020248197A1 - Saturation flow estimation for signalized intersections using vehicle trajectory data

Info

Publication number: WO2020248197A1
Application number: PCT/CN2019/091153
Authority: WO
Inventors: Jianfeng Zheng; Xianghong Liu
Original assignee: Beijing Didi Infinity Technology And Development Co., Ltd.
Priority date: 2019-06-13
Filing date: 2019-06-13
Publication date: 2020-12-17
Also published as: CN111183464B; CN111183464A

Abstract

The systems and methods for analyzing traffic data. The system may include at least one storage device configured to store instructions and at least one processor configured to execute the instructions to perform operations. The operations may include receiving, through a communication interface, trajectory data relating to a plurality of vehicle movements with respect to an intersection. The operations may also include determining a cycle length of the intersection based on the trajectory data. The operations may further include determining time-distance relationships for the vehicle movements based on the cycle length. In addition, the operations may include detecting a shockwave based on the time-distance relationships. Moreover, the operations may include determining a saturation flow of the intersection based on the shockwave.

Description

SATURATION FLOW ESTIMATION FOR SIGNALIZED INTERSECTIONS USING VEHICLE TRAJECTORY DATA

TECHNICAL FIELD

The present disclosure relates to traffic control at intersections, and more particularly, to systems and methods for estimating a saturation flow for a signalized intersection using vehicle trajectory data.

BACKGROUND

In traffic control, saturation flow is an important road traffic performance measure for evaluating the capacity or efficiency of an intersection. Saturation flow relates to the number of vehicles passing through an intersection in a flow of traffic, and it is used extensively in signalized intersection control and design. Traditionally, saturation flow is estimated based on intersection surveys, including observation of actual or recorded traffic flows and manually counting the number of vehicles. Such a traditional method is inefficient and time consuming.

Embodiments of the disclosure improve the traditional method by utilizing vehicle trajectory data, which are not traditionally used in saturation flow estimation. Vehicle trajectory data have become available as a viable information source thanks to the proliferation of app-based ride hailing and ride sharing services, where vehicle trajectory data can be collected based on, for example, vehicle positioning information and map information. Utilizing vehicle trajectory data for saturation flow estimation provides an efficient and scalable new approach for analyzing traffic data.

SUMMARY

Embodiments of the disclosure provide a system for analyzing traffic data. The system may include at least one storage device configured to store instructions. The system may also include at least one processor configured to execute the instructions to perform operations. The operations may include receiving, through a communication interface, trajectory data relating to a plurality of vehicle movements with respect to an intersection. The operations may also include determining a cycle length of the intersection based on the trajectory data. The operations may further include determining time-distance relationships for the vehicle movements based on the cycle length. In addition, the operations may include detecting a shockwave based on the time-distance relationships. Moreover, the operations may include determining a saturation flow of the intersection based on the shockwave.

Embodiments of the disclosure also provide a method for analyzing traffic data. The method may include receiving trajectory data relating to a plurality of vehicle movements with respect to an intersection. The method may also include determining a cycle length of the intersection based on the trajectory data. The method may further include determining time-distance relationships for the vehicle movements based on the cycle length. In addition, the method may include detecting a shockwave based on the time-distance relationships. Moreover, the method may include determining a saturation flow of the intersection based on the shockwave.

Embodiments of the disclosure further provide a non-transitory computer-readable medium having instructions stored thereon that, when executed by at least one processor, causes the at least one processor to perform a method for analyzing traffic data. The method may include receiving trajectory data relating to a plurality of vehicle movements with respect to an intersection. The method may also include determining a cycle length of the intersection based on the trajectory data. The method may further include determining time-distance relationships for the vehicle movements based on the cycle length. In addition, the method may include detecting a shockwave based on the time-distance relationships. Moreover, the method may include determining a saturation flow of the intersection based on the shockwave.

It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an exemplary scene of intersection traffic, according to embodiments of the disclosure.

FIG. 2 illustrates a schematic diagram of an exemplary vehicle equipped with a trajectory sensing system, according to embodiments of the disclosure.

FIG. 3 illustrates a block diagram of an exemplary system for analyzing traffic data, according to embodiments of the disclosure.

FIG. 4. illustrates a flowchart of an exemplary method for analyzing traffic data, according to embodiments of the disclosure.

FIG. 5 illustrates a flowchart of an exemplary method for detecting a shockwave, according to embodiments of the disclosure.

FIG. 6 shows an exemplary distribution of the distances between motion-change points and a candidate shockwave line, according to embodiments of the disclosure.

FIGS. 7-10 show an exemplary shockwave detection method based on a T-S figure, according to embodiments of the disclosure.

FIGS. 11-12 show an exemplary method of calculating a saturation flow, according to embodiments of the disclosure.

FIG. 13 illustrates an exemplary map of a movement based on GPS data, according to embodiments of the disclosure.

FIG. 14 shows an exemplary trajectory of a movement, according to embodiments of the disclosure.

FIG. 15 illustrates an exemplary map showing saturation flow estimations at multiple intersections, according to embodiments of the disclosure.

DETAILED DESCRIPTION

Reference will now be made in detail to the exemplary embodiments, examples of which are illustrated in the accompanying drawings. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same or like parts.

Embodiments of the present disclosure provide systems and methods to estimate a saturation flow of an intersection using trajectory data. The intersection may have fixed signal timing. Based on the trajectory data, a cycle length may be estimated. Then, the trajectory data may be projected to the cycle length to obtain time in a cycle and to generate a time-distance figure (T-S figure) of vehicle movements. A shockwave may be detected in the T-S figure assuming that the vehicles are controlled by a signal light. A valid detected shockwave may provide information including a shockwave speed, a location of a stop bar, and a green light start time. Combining the shockwave speed, a departure speed, and a jam density (assumed to be a constant) , the value of the saturation flow can be determined, which reflects vehicle movement capacity at the intersection. In traffic control, saturation flows can be used to quantify the capacity of intersections to quickly identify low-efficient intersections.

FIG. 1 illustrate an exemplary scene depicting traffic conditions at an intersection. As shown in FIG. 1, multiple vehicles may travel along intersecting

roads

102 and 103 and may be controlled by a signal light 106 at an intersection 104. Intersection 104 may include a stop bar 108 in each direction, which may serve as a landmark for vehicles to stop, waiting for the green light. Some vehicles, such as vehicle 110, may be equipped with a trajectory sensing system 112, which may obtain trajectory data including the location and time information relating to the movement of vehicle 110. The trajectory data may be sent to a server 130. In another example, a driver of a vehicle, such as vehicle 120, may use a terminal device 122 (e.g., a mobile phone) to run a mobile program capable of collecting trajectory data. For instance, the driver may use terminal device 122 to run a ride hailing or ride sharing mobile application, which may include software modules capable of obtaining location, time, speed, and/or pose information of vehicle 120. Terminal device 122 may communicate with server 130 to send the trajectory data to server 130. It is noted that, although intersection 104 shown in FIG. 1 is an intersection between two roads with a traffic light placed in the center, such simplification is exemplary and for illustration purposes only. Embodiments disclosed herein are applicable to any forms of intersections with any suitable configuration of traffic lights.

FIG. 2 illustrates a schematic diagram of an exemplary vehicle 110 having trajectory sensing system 112, according to embodiments of the disclosure. It is contemplated that vehicle 110 may be an electric vehicle, a fuel cell vehicle, a hybrid vehicle, or a conventional internal combustion engine vehicle. Vehicle 110 may have a body 116 and at least one wheel 118. Body 116 may be any body style, such as a sports vehicle, a coupe, a sedan, a pick-up truck, a station wagon, a sports utility vehicle (SUV) , a minivan, or a conversion van. In some embodiments, vehicle 110 may include a pair of front wheels and a pair of rear wheels, as illustrated in FIG. 2. However, it is contemplated that vehicle 110 may have more or less wheels or equivalent structures that enable vehicle 110 to move around. Vehicle 110 may be configured to be all wheel drive (AWD) , front wheel drive (FWR) , or rear wheel drive (RWD) . In some embodiments, vehicle 110 may be configured to be operated by an operator occupying the vehicle, remotely controlled, and/or autonomously controlled.

As illustrated in FIG. 2, vehicle 110 may be equipped with trajectory sensing system 112. In some embodiments, trajectory sensing system 112 may be mounted or attached to the outside of body 116. In some embodiments, trajectory sensing system 112 may be equipped inside body 116, as shown in FIG. 2. In some embodiments, trajectory sensing system 112 may include part of its component (s) equipped outside body 116 and part of its component (s) equipped inside body 116. It is contemplated that the manners in which trajectory sensing system 112 can be equipped on vehicle 110 are not limited by the example shown in FIG. 2, and may be modified depending on the types of sensor (s) included in trajectory sensing system 112 and/or vehicle 110 to achieve desirable sensing performance.

In some embodiments, trajectory sensing system 112 may be configured to capture live data as vehicle 110 travels along a path. For example, trajectory sensing system 112 may include a navigation unit, such as a GPS receiver and/or one or more IMU sensors. A GPS is a global navigation satellite system that provides location and time information to a GPS receiver. An IMU is an electronic device that measures and provides a vehicle’s specific force, angular rate, and sometimes the magnetic field surrounding the vehicle, using various inertial sensors, such as accelerometers and gyroscopes, sometimes also magnetometers.

Vehicle 110 may communicate with server 130 to transmit the sensed trajectory data to server 130. Server 130 may be a local physical server, a cloud server (as illustrated in FIGS. 1 and 2) , a virtual server, a distributed server, or any other suitable computing device. Consistent with the present disclosure, server 130 may store a database of trajectory data received from multiple vehicles, which can be used to estimate saturation flows at intersections.

Server 130 may communicate with vehicle 110, and/or components of vehicle 110 (e.g., trajectory sensing system 112) via a wired or wireless network, such as a Local Area Network (LAN) , a Wireless Local Area Network (WLAN) , a Wide Area Network (WAN) , wireless networks such as radio waves, a cellular network, a satellite communication network, and/or a local or short-range wireless network (e.g., Bluetooth ^TM) .

FIG. 3 shows an exemplary server 130, according to embodiments of the disclosure. Consistent with the present disclosure, server 130 may receive trajectory data 302 from one or more vehicles (e.g., collected by trajectory sensing system 112 and/or terminal device 122) . Trajectory data 302 may include vehicle location and time information that describes a movement trajectory of a vehicle.

In some embodiments, as shown in FIG. 3, server 130 may include a communication interface 310, a processor 320, a memory 330, and a storage 340. In some embodiments, server 130 may have different modules in a single device, such as an integrated circuit (IC) chip (implemented as an application-specific integrated circuit (ASIC) or a field-programmable gate array (FPGA) ) , or separate devices with dedicated functions. In some embodiments, one or more components of server 130 may be located in a cloud, or may be alternatively in a single location (such as inside vehicle 110 or a mobile device) or distributed locations. Components of server 130 may be in an integrated device, or distributed at different locations but communicate with each other through a network (not shown) .

Communication interface 310 may send data to and receive data from a vehicle or its components such as trajectory sensing system 112 and/or terminal device 122 via communication cables, a Wireless Local Area Network (WLAN) , a Wide Area Network (WAN) , wireless networks such as radio waves, a cellular network, and/or a local or short-range wireless network (e.g., Bluetooth ^TM) , or other communication methods. In some embodiments, communication interface 310 can be an integrated services digital network (ISDN) card, cable modem, satellite modem, or a modem to provide a data communication connection. As another example, communication interface 310 can be a local area network (LAN) card to provide a data communication connection to a compatible LAN. Wireless links can also be implemented by communication interface 310. In such an implementation, communication interface 310 can send and receive electrical, electromagnetic or optical signals that carry digital data streams representing various types of information via a network.

Consistent with some embodiments, communication interface 310 may receive trajectory data 302. Communication interface 310 may further provide the received trajectory data 302 to storage 340 for storage or to processor 320 for processing.

Processor 320 may include any appropriate type of general-purpose or special-purpose microprocessor, digital signal processor, or microcontroller. Processor 320 may be configured as a stand-alone processor module dedicated to analyzing traffic data. Alternatively, processor 320 may be configured as a shared processor module for performing other functions unrelated to traffic data analysis.

As shown in FIG. 3, processor 320 may include multiple modules, such as a cycle length estimation unit 322, a shockwave detection unit 324, and a saturation flow calculation unit 326, and the like. These modules (and any corresponding sub-modules or sub-units) can be hardware units (e.g., portions of an integrated circuit) of processor 320 designed for use with other components or software units implemented by processor 320 through executing at least part of a program. The program may be stored on a computer-readable medium, and when executed by processor 320, it may perform one or more functions or operations. Although FIG. 3 shows units 322-326 all within one processor 320, it is contemplated that these units may be distributed among multiple processors located near or remotely with each other.

Memory 330 and storage 340 may include any appropriate type of mass storage provided to store any type of information that processor 320 may need to operate. Memory 330 and/or storage 340 may be a volatile or non-volatile, magnetic, semiconductor, tape, optical, removable, non-removable, or other type of storage device or tangible (i.e., non- transitory) computer-readable medium including, but not limited to, a ROM, a flash memory, a dynamic RAM, and a static RAM. Memory 330 and/or storage 340 may be configured to store one or more computer programs that may be executed by processor 320 to perform functions disclosed herein. For example, memory 330 and/or storage 340 may be configured to store program (s) that may be executed by processor 320 to analyze traffic data.

Memory 330 and/or storage 340 may be further configured to store information and data used by processor 320. For instance, memory 330 and/or storage 340 may be configured to store trajectory data 302 provided by trajectory sensing system 112 and/or terminal device 122. The various types of data may be stored permanently, removed periodically, or disregarded immediately after each frame of data is processed.

FIG. 4 illustrates a flowchart of an exemplary method 400 for analyzing traffic data, according to embodiments of the disclosure. In some embodiments, method 400 may be implemented by server 130. However, method 400 is not limited to that exemplary embodiment. Method 400 may include steps S410-S450 as described below. It is to be appreciated that some of the steps may be optional to perform the disclosure provided herein. Further, some of the steps may be performed simultaneously, or in a different order than shown in FIG. 4.

In step S410, processor 320 may receive trajectory data 302 from one or more vehicles (e.g., vehicles 110 and 120) through communication interface 310. For example, trajectory sensing system 112 may capture trajectory data 302 including location and time information and provide trajectory data 302 to processor 320 via communication interface 310. In another example, terminal device 122 may collect trajectory data 302 and upload trajectory data 302 to server 130 through communication interface 310. As a result, processor 320 may receive trajectory data 320. Trajectory data 302 may be stored in memory 330 and/or storage 340 as input data for performing traffic analysis such as saturation flow estimation. In some embodiments, trajectory data 302 may be related to a plurality of vehicle movements (e.g., vehicles 110 and 120) with respect to an intersection (e.g., intersection 104) .

In step S420, processor 320 may determine a cycle length of the intersection based on trajectory data 302. In some embodiments, processor 320 may project the trajectory data to an estimation of the cycle length to obtain a time variable indicating a time point of passing a predetermined landmark (e.g., stop bar 108) of the intersection and determine the cycle length by minimizing a variation of the time variable over a plurality of vehicle movements. For example, assume that t _i, j is the time when the ith vehicle passes through a stop bar of movement j, then the cycle length C can be estimated by minimizing the sum of the coefficient of variation of each movement after projecting the t _i, j to the cycle C, as follows:

where Var () and Average () are the function to calculate the variance and mean value of a corresponding series. Coefficient of variation (CV) quantifies the degree of concentration of a series in different scale so minimizing the sum of CV of all the movements is equivalent to make the t _i, j as concentrated as possible for each movement after projecting the t _i, j to a cycle C. The set of t ^ref is to avoid the situation that t _i, j is split into the start and the end of the cycle when projecting them in a cycle C.

In step S430, processor 320 may determine time-distance relationships (e.g., in a form of a Time-Distance figure, or T-S figure for short) for vehicle movements based on the cycle length. For example, processor 320 may determine the time-distance relationships by projecting the trajectory data to a single cycle according to the determined cycle length. FIG. 7 illustrates an exemplary T-S figure generated by the operations in step S430.

In step S440, processor 320 may detect a shockwave based on the time-distance relationships. In some embodiments, step S440 may further include sub-steps, as shown in FIG. 5. Referring to FIG. 5, step S440 may include sub-steps S510-S580. In sub-step S510, processor 320 may generate a T-S figure (e.g., FIG. 7) of a movement based on the time-distance relationships determined in step S430. In sub-step S520, processor 320 may select motion-change points based on the T-S figure. In some embodiments, the motion-change points may include stop-to-go points for detecting departure shockwaves. In the following, an exemplary method of selecting stop-to-go points is discussed in connection with FIG. 7.

Referring to FIG. 7, assume that each trajectory shown in FIG. 7 is composed of time-space points with a T-second sampling period. Then, the speed of each point can be calculated using a local point and its adjacent point. An vehicle may be regarded as in stop status when the speed is less than a threshold. To reduce noise, the stop duration may be set to be more than 5 seconds, otherwise the stop is considered to be too short and discarded. Using this threshold, processor 320 may identify those points where the status of the trajectory changes from stop to go. FIG. 8 shows exemplary motion-change points selected using the above method. The selected motion-change points may be recorded as:

{ { (x ₁₁, y ₁₁) , (x ₁₂, y ₁₂) ,... } ,..., { (x _i1, y _i1) ,... (x _ij, y _ij) ,... } ... } (2)where (x _ij, y _ij) refers to the jth motion-change point of ith trajectory. It is noted that not all of these points can be used for shockwave line fitting because some of them may be caused by other reasons such as lane-change or other noise. Therefore, further processing is needed to select those motion-change points that are used for fitting the shockwave line, which may be referred to as shockwave points.

In sub-step S530, processor 320 may determine candidate shockwave lines using a modified Random Sample Consensus (RANSAC) method. In this sub-step, a rough selection of candidate shockwave lines is performed. In the rough selection procedure, two points may be randomly selected as (x _ij, y _ij) and (x _pq, y _pq) . The line crosses these two points can be written as:

y (ij, pq) =k (ij, pq) ·x+b (ij, pq) (3)

Considering that the time in cycle is periodic, the candidate shockwave lines may be a series of lines with a cycle equals to the cycle length of the signal timing:

Y (ij, pq) =y (ij, pq, n) =k (ij,pq) · (x+n·T) +b (ij, pq) n=0, ±1, ±2,... (4)

The goal of the selection is to select the series of lines whose neighbor has the largest number of the motion-change points. Thus, the objective function can be written as:

N (Y (ij, pq) , ∈) →Max, i≠j or p≠q (5)

where N (Y (ij, pq) , ∈) is the number of the motion-change points in the neighbor of the series of lines determined by (x _ij, y _ij) and (x _pq, y _pq) . ∈ refers to the range of the neighborhood. In other words, the series of candidate shockwave lines are determined by maximizing the number of neighboring motion-change points for each candidate shockwave line. FIG. 9 shows exemplary candidate shockwave lines with a cycle T obtained using the above-described modified RANSAC algorithm.

In sub-step S540, processor 320 may determine a shockwave area and corresponding shockwave points based on the rough selection of candidate shockwave lines. Suppose that Y ₀=y ₀ (n) is the selected series of candidate shockwave lines determined in sub-step S530, processor 320 may determine the distance between each motion-change point to the series of candidate shockwave lines as follows:

υ _ij (n) =F (Y ₀=y ₀ (n) , (x _ij, y _ij) ) (6)

where v _ij (n) is the distance between point (x _ij, y _ij) to line y ₀ (n) . For the motion-change points of each trajectory, processor 320 may choose the closest point to the candidate shockwave line as:

where v _t is a threshold that is set to meet the requirement:

where k is the slope of the series of the candidate shockwave lines and T is the cycle length. In some embodiments, choosing the closest point of each trajectory to the candidate shockwave line may guarantee that each trajectory can only contribute at most one point, otherwise it may undermine the regression of the shockwave. The condition |v _i (n) |＜v _t is to set the range for each candidate shockwave line of the series when projecting the motion-change points thereto.

The distribution of |v _i (n) | may be utilized to determine a valid vertical range of the shockwave. FIG. 6 shows an exemplary distribution |v _i (n) | of the distances between motion-change points and a candidate shockwave line. The dashed-line denotes the selected vertical range of the shockwave. Similarly, the horizontal range toward the shockwave may also be determined in this way. Thus, the valid shockwave area can be determined and all the motion-change points falling within this area may be selected as shockwave points. For example, FIG. 10 shows exemplary shockwave points.

In sub-step S550, processor 320 may detect the shockwave by fitting a shockwave line to the shockwave points using a line regression method. In some embodiments, shockwave points in different cycles may be transformed to the same cycle before performing regression. Various line regression method may be used, for example, a Principal Component Analysis (PCA) method may be used to fit the shockwave line using the shockwave points. When applying the PCA method, the direction of the vector of the PC1 (Principal Component 1) can be regarded as the slope of the shockwave line and the weight of PC1 can be used to quantify the linearity of the shockwave points. The PCA method is better than the least square method in this application because the regression goal of PCA is to minimize the distance between the motion-change points and the shockwave line while the least square method is to minimize the horizontal error (∑| _yi-y′ _i| ²→Min) . FIG. 10 shows an exemplary shockwave as a result of the regression.

The shockwave may provide much information of the movement: the slope of the shockwave can be used as the shockwave speed while the time and distance of the start of the shockwave can be used as the green start time and the location of the stop bar.

In sub-step S560, processor 320 may validate the shockwave based on at least one of a vertical variance of the shockwave points or a ratio of the shockwave points to the motion-change points. For example, the less the vertical variance and the more the ratio, the more likely that the detected shockwave is valid. Thus, either or both of these values may be used to validate the detected shockwave. In addition, a too short queue length may undermine the regression of the shockwave line and the accuracy of the shockwave speed. Therefore, a queue length threshold and a PC1 weight threshold may also be set to improve the accuracy of the shockwave speed estimation.

Besides the departure shockwave caused by green light, there may be other departure shockwaves caused by other reasons, such as a left-turn waiting area and a reversible lane.

Processor 320 may determine whether the detected shockwave is valid. If so, process may proceed to sub-step S570, in which all the shockwave points within the range of the valid shockwave may be removed and then the process may be performed again to detect another shockwave using the remaining motion-change points until the detected shockwave is not valid. Then in sub-step S580, all the valid shockwave (s) may be output.

Returning back to FIG. 4, after processor 320 detects one or more shockwaves in S440, method 400 may proceed to step S450, in which processor 320 may determine a saturation flow based on the shockwave. FIGS. 11 and 12 show an exemplary method to calculate the saturation flow. For example, processor 320 may calculate the shockwave speed ω and the location of the stop bar. Using the location of the stop bar, an average departure speed v, indicating a forward free flow speed from the starting point when the signal light turns green until the crossing point at the stop bar can be calculated. The average distance interval between vehicles may be regarded as a constant s ₀. The saturation flow may be equal to the flow of each lane when releasing the queue. As shown in FIG. 11, assume that queue length is l, it will take time t for these vehicles to pass through the stop bar,

The saturation flow q ₀ is

where s ₀ may be considered as a constant, for example,

s ₀=7m/pcu (11)

In some embodiments, trajectory data 302 may be generated when vehicle drivers use ride hailing or ride sharing services such as Didichuxing ^TM application to take passengers. The raw format of the trajectory data may include time stamp and location information with a 3 second sampling period. The trajectory data can be matched to the road by utilizing the geometric information of a map. In this way, the raw trajectory data can be converted to distance to the intersection x _i (t) , which means that at time t, the distance to the intersection for trajectory i is x _i (t) .

To evaluate the performance of different movements of the intersection separately, the trajectory data may be divided into different movements. FIGS. 13 and 14 are exemplary trajectory data of a movement. The GPS information including longitude and latitude of the trajectory data may be converted to the distance to the intersection. The zero point refers to the GPS point of the intersection from the map data, which may or may not reflect the location of the stop bar.

FIG. 15 shows an exemplary map showing saturation flow estimation in part of a city. The dots shown on the map indicate the intersections where saturation flow estimation is conducted, and the color of the dots indicates the degree of saturation. For each intersection, the saturation flow is calculated as a weighted mean of each movement of the intersection over a five-weekday period:

Where q ₀ is the weighted mean of saturation flow of the intersection, q _i is the saturation flow of movement i while n _i is the number of the trajectories.

Another aspect of the disclosure is directed to a non-transitory computer-readable medium storing instructions which, when executed, cause one or more processors to perform the methods, as discussed above. The computer-readable medium may include volatile or non-volatile, magnetic, semiconductor, tape, optical, removable, non-removable, or other types of computer-readable medium or computer-readable storage devices. For example, the computer-readable medium may be the storage device or the memory module having the computer instructions stored thereon, as disclosed. In some embodiments, the computer-readable medium may be a disc or a flash drive having the computer instructions stored thereon.

It will be apparent to those skilled in the art that various modifications and variations can be made to the disclosed system and related methods. Other embodiments will be apparent to those skilled in the art from consideration of the specification and practice of the disclosed system and related methods.

It is intended that the specification and examples be considered as exemplary only, with a true scope being indicated by the following claims and their equivalents.

Claims

A system for analyzing traffic data, comprising:

at least one storage device configured to store instructions; and

at least one processor configured to execute the instructions to perform operations, the operations comprising:

receiving, through a communication interface, trajectory data relating to a plurality of vehicle movements with respect to an intersection;

determining a cycle length of the intersection based on the trajectory data;

determining time-distance relationships for the vehicle movements based on the cycle length;

detecting a shockwave based on the time-distance relationships; and

determining a saturation flow of the intersection based on the shockwave.
The system of claim 1, wherein the operations comprise:

projecting the trajectory data to an estimation of the cycle length to obtain a time variable indicating a time point of passing a predetermined landmark of the intersection; and

determining the cycle length by minimizing a variation of the time variable over the plurality of vehicle movements.
The system of claim 1, wherein the operations comprise:

determining the time-distance relationships by projecting the trajectory data to a cycle according to the determined cycle length.
The system of claim 1, wherein the operations comprise:

selecting motion-change points based on the time-distance relationships.
The system of claim 4, wherein the motion-change points include stop-to-go points.
The system of claim 4, wherein the operations comprise:

determining a series of candidate shockwave lines by maximizing a number of neighboring motion-change points for each candidate shockwave line.
The system of claim 6, wherein the operations comprise:

determining distances between the motion-change points and the series of candidate shockwave lines;

determining a shockwave area based on a distribution of the distances; and

selecting a subset of the motion-change points that fall within the shockwave area as shockwave points.
The system of claim 7, wherein the operations comprise:

detecting the shockwave by fitting a shockwave line to the shockwave points using a line regression method.
The system of claim 8, wherein the operations comprise:

validating the shockwave based on at least one of a vertical variance of the shockwave points or a ratio of the shockwave points to the motion-change points.
The system of claim 1, wherein the operations comprise:

determining a shockwave speed and a location of a stop bar based on the detected shockwave;

determining a departure speed based on the location of the stop bar; and

determining the saturation flow based on the shockwave speed and the departure speed.
A method for analyzing traffic data, comprising:

receiving trajectory data relating to a plurality of vehicle movements with respect to an intersection;

determining a cycle length of the intersection based on the trajectory data;

determining time-distance relationships for the vehicle movements based on the cycle length;

detecting a shockwave based on the time-distance relationships; and

determining a saturation flow of the intersection based on the shockwave.
The method of claim 11, comprising:

projecting the trajectory data to an estimation of the cycle length to obtain a time variable indicating a time point of passing a predetermined landmark of the intersection; and

determining the cycle length by minimizing a variation of the time variable over the plurality of vehicle movements.
The method of claim 11, comprising:

determining the time-distance relationships by projecting the trajectory data to a cycle according to the determined cycle length.
The method of claim 11, comprising:

selecting motion-change points based on the time-distance relationships.
The method of claim 14, comprising:

determining a series of candidate shockwave lines by maximizing a number of neighboring motion-change points for each candidate shockwave line.
The method of claim 15, comprising:

determining distances between the motion-change points and the series of candidate shockwave lines;

determining a shockwave area based on a distribution of the distances; and

selecting a subset of the motion-change points that fall within the shockwave area as shockwave points.
The method of claim 16, comprising:

detecting the shockwave by fitting a shockwave line to the shockwave points using a line regression method.
The method of claim 17, comprising:

validating the shockwave based on at least one of a vertical variance of the shockwave points or a ratio of the shockwave points to the motion-change points.
The method of claim 11, comprising:

determining a shockwave speed and a location of a stop bar based on the detected shockwave;

determining a departure speed based on the location of the stop bar; and

determining the saturation flow based on the shockwave speed and the departure speed.
A non-transitory computer-readable medium having instructions stored thereon, wherein the instructions, when executed by at least one processor, cause the at least one processor to perform a method for analyzing traffic data, the method comprising:

receiving trajectory data relating to a plurality of vehicle movements with respect to an intersection;

determining a cycle length of the intersection based on the trajectory data;

determining time-distance relationships for the vehicle movements based on the cycle length;

detecting a shockwave based on the time-distance relationships; and

determining a saturation flow of the intersection based on the shockwave.