Office of Safety and Operations 

Research and Development 

1

Optimizing Vehicle Trajectories at Fixed-Time Traffic Signal Intersections 

using Cooperative Driving Automation (CDA)

© Getty Images Plus.

Automated vehicles communicating with smart traffic signals can 

travel through signalized intersections more safely and efficiently. The 

functionality developed in this project demonstrates CDA’s potential to 

benefit automated vehicles by supporting them as they navigate 

signalized intersections with fixed-time settings. As shown in figure 1, 

vehicles approaching an intersection may share status and intent 

information (such as the vehicle’s current location and speed, the 

intended future path, etc.) with a roadside unit (RSU) and receive signal 

phase and timing (SPaT) inputs from the traffic signals connected to 

the RSU once in range.(1,2)

 SpaT inputs communicate to the vehicle 

current phase and interval for the traffic light and how much time 

remains at that interval. The vehicle can then determine how best to 

proceed based on the intervals. Vehicles can automatically adjust and 

smooth their trajectory to minimize their stopping times by reducing 

their speed ahead of a yellow light change. They can also pass through 

an intersection during a green interval with a higher speed, within 

designated limits. This technology allows for smoother transitions 

through intersections, better flowing traffic patterns, fewer delays, less 

energy consumption, and less backward shock-wave propagation.(3)

Figure 1. Graphic. Vehicles entering a 

signalized intersection.

Improve Energy Efficiency

With reduced stopping and delay and less stop-and-go traffic, general fuel economy may 

improve by up to 30 percent.

(4)

Reduce Travel Delays

With stop-and-go traffic from signalized intersections reduced, road users could experience 

50 percent less stop time during travel, and shorter commute times. Less 

stop-and-go traffic would also contribute to smoother driving experiences.(4)

Maintain Safety

In 2021, 42,939 people were killed in motor vehicle traffic crashes on U.S. roadways. With 

intersections being potentially unpredictable, CDA technology could reduce the chance of 

collision, improving road safety for all users with enhanced awareness.(4)

BENEFITS TO TRANSPORTATION

Source: Federal Highway Administration (FHWA).
2

TITLE OF TECHBRIEF

OPTIMIZING VEHICLE TRAJECTORIES AT FIXED-TIME TRAFFIC SIGNALS INTERSECTIONS USING CDA

EVALUATION OF THE CONCEPT

The research team first conducted simulation experiments to evaluate and fine-tune the developed algorithms for four 

cooperation classes as defined by SAE International® J3216TM.(5) In scenarios where vehicles and infrastructure are 

equipped with CDA technology, the objective of the experiment is for the vehicle to achieve smoother trajectories and 

enter the intersection box at relatively higher speed. This approach results in a reduced departure headway between 

consecutive vehicles, thereby increasing throughput. The results show that the developed algorithms reduce average 

travel delay, fuel consumption, and stopping time at signalized intersections with fixed time traffic signals.

Figure 2 and figure 3 depict vehicle trajectories (space-time motion) for human-driven and CDA vehicles, respectively, 

in a selected lane and the optimal cycle length. The vertical axis represents space in meters, while the horizontal axis 

represents time in seconds. In these graphs, each solid line corresponds to the trajectory of a single vehicle, and a 

change in the line’s slope directly correlates to a change in the vehicle’s speed. For example, as the slope of the line 

increases, the speed of the vehicle also increases and vice versa. These visuals highlight a crucial observation; unlike 

human-driven vehicles, which come to a complete stop and wait at the signal for a signal change before entering the 

intersection, vehicles equipped with automation Level 3 and using Class A(5) cooperation show a smoother flow by 

slowing down before reaching the intersection. These graphs demonstrate that the algorithms developed in this 

research project effectively eliminate stop-and-go traffic patterns and backward shock-wave propagations.(3) This feature 

ultimately enhances the travel experience and reduces traffic time for a vehicle navigating a signalized intersection.

After completing traffic simulation studies, the team carried out multiple rounds of proof-of-concept (PoC) testing using 

full-sized FHWA vehicles and infrastructure equipped with CDA on controlled test tracks. These tests assessed various 

operational aspects, including communication, safety, mobility, and the smoothness of vehicle trajectories. All testing took 

place at the Turner-Fairbank Highway Research Center. Tests evaluated system performance in critical scenarios, such as 

vehicle arrival at an intersection at the beginning or the end of a green light interval. After several initial testing rounds to 

verify the implemented algorithms, the Volpe National Transportation Systems Center led additional testing rounds to 

validate the algorithms and the findings, helping set a foundation for further research and development. 

CDA COOPERATION CLASSES 

Defined in SAE J3216 Standard(5)

 Class A: Status sharing 

 Class B: Intent sharing 

 Class C: Agreement seeking 

 Class D: Prescriptive 

STANDARDS

This technology meets the following standards established by SAE International:

 SAE J3216_202107: Taxonomy and Definitions for Terms Related to CDA for On-Road 

Motor Vehicles.

(5)

 SAE J3016_202104TM: Taxonomy and Definitions for Terms Related to Driving 

Automation Systems for On-Road Motor Vehicles.

(6)

 SAE J2735_202007TM: Vehicle-to-Everything Communications Message Set Dictionary.

(7)

Figure 3. Graph. Trajectory of cooperation Class A vehicles as 

they approach a traffic signal over time.(5)

Source: FHWA.

Figure 2. Graph. Trajectory of human-driven vehicles as 

they approach a traffic signal over time. 

Source: FHWA.
3

USE CASE ARCHITECTURE

While the algorithms were developed and simulations were conducted for all different CDA cooperation classes 

defined in SAE International J3216, the implementation of this use case on the CARMASM ecosystem focuses solely on 

cooperation Class A.(5,8)

 The components of the CARMA ecosystem used in this cooperation class include CARMA 

PlatformSM and the Vehicle-to-Everything (V2X) Hub.(9,10)

 Figure 4 provides a look at how each aspect of the CARMA 

components works together. The V2X Hub broadcasts the SPaT messages, and CARMA Platform estimates the time the 

vehicle can enter and spend at the intersection.(2) In this architecture, vehicles may also share status information via 

the RSU using the basic safety message (BSM) and customized mobility operations messages (MOM) and mobility path 

messages (MPM).(1)

This shared data can potentially enhance the CARMA Platform’s time to enter the intersection estimations by 

leveraging the information of other vehicles.(9) However, due to the CARMA Platform limitation at the field testing 

time, this feature could not be tested and consequently has not been fully implemented. The CARMA Platform then 

controls the vehicle trajectory accordingly to minimize the vehicle stopping time and optimize the vehicle’s energy 

and fuel efficiency.

RESULTS AND LESSONS LEARNED

The results of analyses from testing show that the PoC frameworks meet a set of key objective metrics that the 

research team considered to be related to message processing, communication rates, and algorithm logic. These 

metrics include, in particular, vehicle trajectory sequencing, estimation of the time the vehicles enter the intersection 

during different signal phases, and adherence to specified deceleration and acceleration boundaries. One aspect not 

considered in this test that could be considered in future testing is vehicle-to-vehicle communication. While the team 

identified some limitations through data collection and analysis, these limitations can be addressed as part of future 

CDA program efforts. 

OPTIMIZING VEHICLE TRAJECTORIES AT FIXED-TIME TRAFFIC SIGNALS INTERSECTIONS USING CDA

Figure 4. Graphic. CARMA design and architecture for fixed-time traffic signals use case—

cooperation Class A. (See references 2, 4, 8, 9, 10, and 11.)

Source: FHWA.
TITLE OF TECHBRIEF

For more information, please contact the CDA Program at CDA@dot.gov

OPTIMIZING VEHICLE TRAJECTORIES AT FIXED TIME TRAFFIC SIGNALS INTERSECTIONS USING CDA

TO LEARN MORE AND FOLLOW UPDATES

CDA Program

https://www.fhwastol.org/

V2X GitHub

https://github.com/

usdot-fhwa-OPS/ 

V2X-Hub

CARMA Platform

https://github.com/usdotfhwa-stol/carma-platform

Applying vehicle-to-vehicle communications in a fixed time traffic signal 

environment allows for higher scale deployments, which would result in increased 

confidence and reliability when quantifying individuals and systems.

Extending this use case to test in a mixed-traffic environment, where only part of 

the traffic is equipped with CDA technology, would further research that will 

accelerate industry deployment.

Using more complex components (lane changes, multiple vehicles, vulnerable 

road users, presence of incidents) will help improve the technology.

Large-Scale Testing

Mixed-Traffic Environment

More Dynamic Situations

4

CONCLUSIONS

This test case proved the benefits of CDA application in signalized intersections with fixed-time settings and helped 

provide a better understanding of its advantages. Potential for future work remains high. In particular, the developed 

framework can be significantly improved by completing further research in the following scenarios:

REFERENCES

1. AASHTO, ITE, and NEMA. 2020. National Transportation Communications for ITS Protocol Object Definitions for Roadside Units (RSUs). NTCIP 1218 v01.38. Washington, DC: American 

Association of State Highway and Transportation Officials; Washington, DC: Institute of Transportation Engineers; and Rosslyn, VA: National Electrical Manufacturers Association. 

https://www.ntcip.org/file/2021/01/NTCIP-1218v0138-RSU-toUSDOT-20200905.pdf, last accessed May 23, 2023.

2. Intelligent Transportation Systems Joint Program Office. n.d. ITS Deployment Evaluation: Signal Phase and Timing (SPaT). Washington, DC: U.S. Department of Transportation (USDOT). 

https://www.itskrs.its.dot.gov/sites/default/files/doc/07_SPaT%20Challenge_FINAL%20508%20VERSION_06_23_21.pdf, last accessed October 24, 2023.

3. S. Soleimaniamiri, X. Li, H. Yao, A. Ghiasi, G. Vadakpat, P. Bujanovic, T. Lochrane, J. Stark, K. Blizzard, D. Hale, and S. Racha. 2021. Cooperative Automation Research: CARMA Proof-of-Concept 

Transportation System Management and Operations Use Case 2. Report No. FHWA-HRT-21-069. Washington, DC: Federal Highway Administration.

4. S. Soleimaniamiri, X. Li, H. Yao, A. Ghiasi, G. Vadakpat, P. Bujanovic, and T. Lochrane. Forthcoming. CARMA Proof-of-Concept TSMO Use Case 2 Algorithm. Washington, DC: Federal Highway 

Administration.

5. SAE International. 2020. Taxonomy and Definitions for Terms Related to Cooperative Driving Automation for On-Road Motor Vehicles. SAE J3216_202107. Warrendale, PA: SAE International. 

https://www.sae.org/standards/content/j3216_202107/, last accessed October 19, 2020.

6. SAE International. 2018. Taxonomy and Definitions for Terms Related to Driving Automation Systems for On-Road Motor Vehicles. SAE J3016_202104. Warrendale, PA: SAE International. 

https://www.sae.org/standards/content/j3016_202104, last accessed May 30, 2023.

7. SAE International. 2020. V2X Communications Message Set Dictionary. SAE J2735_202007. Warrendale, PA: SAE International. https://www.sae.org/standards/content/j2735_202007, 

last accessed June 21, 2022.

8. USDOT. n.d. “CARMA” (web page). https://its.dot.gov/cda/, last accessed May 30, 2023.

9. FHWA. n.d. “carma platform” (software and configuration files in GitHub repository). https://github.com/usdot-fhwa-stol/carma-platform, last accessed April 12, 2023.

10. FHWA. 2023. “V2X-Hub” (software and configuration files in GitHub repository). https://github.com/usdot-fhwa-OPS/V2X-Hub, last accessed April 13, 2023.

11. AASHTO, ITE, and NEMA. 2019. National Transportation Communications for ITS Protocol Object Definitions for Actuated Signal Controllers (ASC) Interface. NTCIP 1202 v03A. 

Washington, DC: American Association of State Highway and Transportation Officials; Washington, DC: Institute of Transportation Engineers; and Rosslyn, VA: National Electrical 

Manufacturers Association. https://www.ntcip.org/file/2019/07/NTCIP-1202v0328A.pdf, last accessed May 2019.

FHWA-HRT-24-029

HRSO-40/12-23(200)E

Recommended citation: Federal Highway Administration. Adaptive Traffic Signal Control 

Optimization in a Cooperative Driving Automation (CDA) Environment (Washington, DC: 2023) 

https://doi.org/10.21949/1521469