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Smart Sensors and Infrastructures for Transportation
(July 29, 2021)

Adaptive and Multi-Path Progression Signal Control Under Connected Vehicle Environment
Presenter: Qinzheng Wang
Presenter’s Org: University of Utah Department of Civil & Environmental Engineering

T3 webinars are brought to you by the Intelligent Transportation Systems (ITS) Professional Capacity Building (PCB) Program of the U.S. Department of Transportation (USDOT)’s ITS Joint Program Office (JPO). References in this webinar to any specific commercial products, processes, or services, or the use of any trade, firm, or corporation name is for the information and convenience of the public, and does not constitute endorsement, recommendation, or favoring by the USDOT.

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Slide 1: Adaptive and Multi-Path Progression Signal Control Under Connected Vehicle Environment

ITS Professional Capacity Building Program
T3e Webinar
Smart Sensors and Infrastructures for Transportation
July 29, 2021

Qinzheng Wang
Department of Civil & Environmental Engineering
University of Utah
07/29/2021

[This slide contains two images: (1) the U.S. DOT triskelion and (2) the logo of the Utah Transportation and Artificial Intelligence Lab.]

Slide 2: Outline

1. Background

↓

2. Sensor-based Traffic Signal Control

↓

3. Numerical Examples

↓

4. Conclusions

Slide 3: Background

Connected Vehicles (CV)
↓	↓
Vehicle to vehicle (v2v)	Vehicle to infrastructure (v2I)

On-board Sensors equipped in vehicles are providing various vehicle sensor data (VSD) such as the CAV’s GPS location, speed and moving direction (trajectory)

Roadside Sensors can provide various information, such as traffic signal timing information, for vehicle control.

[This slide contains five images: (1) a photo showing vehicle-to-vehicle connections, (2) a photo showing vehicle-to-infrastructure connections, (3) a photo showing on-board sensors, (4) a photo showing roadside sensors, (5) a photo of signal controllers.]

Slide 4: Background and Motivations

Signal coordination: a method of timing groups of traffic signals along an arterial to provide for the smooth movement of traffic with minimal stops.

Provided progression for one through path or two through paths and assuming that flows along those paths (OD flow) are highest.

Design a fixed offset plan during the whole control period.

[This slide contains two images: (1) a graphic of a road showing a car going inbound and a car going outbound and (2) a graphic showing outbound traffic.]

Slide 5: Background and Motivations

• Provide progression to multiple paths with high volume (critical paths)
• Change coordination plan

[This slide contains one graphic showing the inbound and outbound movements of the critical paths.]

Slide 6: Outline

1. Background

↓

2. Sensor-based Traffic Signal Control

↓

3. Numerical Examples

↓

4. Conclusions

Slide 7: Sensor-based Traffic Signal Control

Slide 8: Sensor-based Traffic Signal Control

Intersection Level

Vehicle arrival flow rate:	μl,i(k, j) = 1/C * ql,i(j) ∀l,j	(1)
Turning flow:	ql,i(j) = 1/Ν ΝΣn=1 qi,j(j - n)	(2)
	ql,i(j) = qcl,i(j) / pl,i(j)	(3)
Market penetration rate:	pl,i(j) = Νc,j / Νall,j	(4)
	Νall,j = Lq,j / Leƒƒ	(5)

Slide 9: Sensor-based Traffic Signal Control

Case 1: More than one CAV in the queue	Lu = υq,l * (t - tc1,l)	(6)
	υq,l = Lc1,l - Lc2,l / tc1,l - tc2,l	(7)
	Lq,l = Lc1,l + Lu	(8)
Case 2: Only one CAV in the queue	υq,l = Lc1,l / tc1,l - tr,l	(9)
Case 3: No CAV in the queue	We simplify the lane flow of current cycle under this condition by the average lane flow of previous several cycles.

Slide 10: Sensor-based Traffic Signal Control

Model 1

minΣjj=1dl(j)		(10)
dl(j) = ΣLl=1Σck=1Ql,l(k,j) * Δt ∀l,j	Total intersection delay	(11)
Ql,i(k,j) = max(Qi,j(k - 1,j) + μl,i(k,j) - rl,i(k,j), 0) ∀l,j	Queue length	(12)
μl,i(k,j) = 1/c * qι,i(j) ∀l,j	Vehicle arrival rate	(13)
rl,i(k,j) = {Sl,i*Δt 0 ∀l,j	Saturation flow rate	(14)
Ql,i(0,j) = τl,i(0,j -1) ∀l,j	Initial queue length at the start of each cycle	(15)
p=ΝΣp=1(gi,p(k) + li,p(k)) = c(k)	Timing plan constraints	(16)
gmin≤gl,m(k)≤gmax		(17)
gi,m(k - 1) - Δgi≤gi,m(k)≤gi,m(k - 1) + Δgi		(18)

Slide 11: Sensor-based Traffic Signal Control

Dynamic programming

Basic features: stage; state variable; decision variable; value function

Stage: phases

Decision variable: green time

State variable: total allocated time when each stage is completed

Value function: total delay

[This slide contains one image of a map showing dynamic programming of sensor-based traffic signal control.]

Slide 12: Sensor-based Traffic Signal Control

Coordination level

max(ΣiΣpωp(h)bp,l(j) + ΣiΣpω‾p(h)b‾p,i(h))		(19)
b‾p,i(h) = max(b‾r,p,i(h) - b‾l,p,i(h), 0)	Green bandwidth	(20)
b‾p,i(h) = max(b‾r,p,i(h) - b‾l,p,i(h), 0)		(21)
br,p,i(h) = min(tr,p,i(h) + ti,i+1(h),tr,p,i+1(h))	Right edge and left edge of the green band	(22)
bl,p,i(h) = max(tl,p,i(h) + ti,i+1(h),tl,p,i+1(h))		(23)
b‾r,p,i(h) = min(tr,p,i+1(h) + ti,i+1(h),ti,i+1(h),tr,p,i(h))		(24)
b‾l,p,i(h) = max(tl,p,i+1(h) + ti,i+1(h),tl,p,i(h))		(25)
tl,p,i(h) = ΣmΣnβm,p,i*φm,n*gi,m(h) +Θi(h)	Start and end of the green times	(26)
tr,p,i(h) = ΣmΣnβm,p,i*φm,n*gi,m(h) + Σmβm,p,i*gi,m(h) + Θi(h)		(27)

Slide 13: Sensor-based Traffic Signal Control

If the green band for a path is not continuous between intersections along an arterial, vehicles may need to stop several times when traveling along this path, which negatively impacts on the effectiveness of the coordination system.

[This slide contains two graphs: (1) a graph showing sensor-based traffic signal control with three offset bars running horizontally labeled “Intersection” (2) a graph showing sensor-based traffic signal control with three offset bars running horizontally each labeled “Intersection.”]

Slide 14: Sensor-based Traffic Signal Control

bl,p,i(h)<br,p,i+1(h) - ti,i+1(h)	(28)
br,p,i(h)>bl,p,i+1(h) - ti,i+1(h)	(29)
b‾l,p,i+1(h)<b‾r,p,i(h) - ti,i+1(h)	(30)
b‾l,p,i+1(h)<b‾r,p,i(h) - ti,i+1(h)	(31)
Θi-1(h) - ΔΘi≤Θi(h)≤Θi-1(h)+ΔΘi	(32)

[This slide contains two graphs: (1) a graph showing sensor-based traffic signal control with four offset bars running horizontally labeled “Intersection” (2) a graph showing sensor-based traffic signal control with four offset bars running horizontally each labeled “Intersection.”]

Slide 15: Sensor-based Traffic Signal Control

Dynamic programming

Stage: intersections

Decision variable: offset

State variable: feasible new offset

Value function: green band width

[This slide contains a map showing dynamic programing of sensor-based traffic signal control.]

Slide 16: Outline

1. Background

↓

2. Sensor-based Traffic Signal Control

↓

3. Numerical Examples

↓

4. Conclusions

Slide 17: Numerical Examples

[This slide contains two images: (1) a bird’s eye view photo of a map and (2) a illustration of road intersections.]

Slide 18: Numerical Examples

Three control systems

Fixed progression control system: the coordination parameters including phase split, cycle length and offset are determined by TOC and are applied in daily traffic management and operation. The signal timing plan is shown in the figure and the offset of the four intersections are 45s, 98s, 49s, and 96s from west to east, respectively.

Adaptive control system: only the developed adaptive traffic signal control system is applied in the simulated network. In this case, detectors are installed behind the stop bar to get the turning flow of each intersection.

Proposed control system: Following the control logic, adaptive traffic signal control and dynamic progression control are both implemented. The proposed control system is tested with four scenarios of 25%, 50%, 75% and 100% CAV market penetration rate.

Slide 19:

Time Period	Critical paths
1200-1800	Path 1; path 2; path 4; path 5
1800-2400	Path 1; path 2; path 4; path 5
2400-3000	Path 1; path 2; path 4; path 5
3000-3600	Path 1; path 2; path 4; path 5
3600-4200	Path 1; path 3; path 4; path 5
4200-4800	Path 1; path 3; path 4; path 5

[This slide contains a graphic of the 5 critical paths in a roadway.]

Slide 20: Numerical Examples

Travel time of critical path

[This slide contains two images: (1) a line graph of average time by simulation time for Path 1 with a line drawing of path 1 on the roadway. (2) a line graph of average time by simulation time for Path 4 with a line drawing of path 4 on the roadway.]

Slide 21: Numerical Examples

[This slide contains three images: (1) a line graph of average time by simulation time for Path 2 with a line drawing of path 2 on the roadway. (2) a line graph of average time by simulation time for Path 3 with a line drawing of path 3 on the roadway. (3) a line graph of average time by simulation time for Path 5 with a line drawing of path 5 on the roadway.]

Slide 22: Numerical Examples

Arterial performance

Arterial performance of proposed and fixed coordination control system

Arterial performance of proposed and adaptive signal control system

Slide 23: Numerical Examples

Sensitivity analysis with various demand level

[This slide contains two graphs: (1) a bar chart of market penetration rate/control strategy with average vehicle delay, (2) a bar chart of market penetration rate/control strategy with average vehicle stop.]

Slide 24: Outline

1. Background

↓

2. Sensor-based Traffic Signal Control

↓

3. Numerical Examples

↓

4. Conclusions

Slide 25: Conclusions

• With the advances in the sensors technology, traffic signals can collect real-time vehicle information including location, speed, acceleration, heading and other vehicle data. Leveraging these enriched data, traffic controllers are able to perform more effectively.
• Developing a real-time control system to adaptively optimize signal control plan to minimize the total vehicle delay for an isolated intersection under different market penetration rates of CAV.
• Regarding low market penetration rate and available CAV information, a method was developed to estimate the vehicle arrival information at the intersection.
• Developing a real-time control system to dynamically optimize offsets of intersections to offer green bandwidth to paths with high volume.

Slide 26: Thank you for your time

Questions?

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