1. Dilemma Zone Protection at An Isolated Signalized Intersection Using Dynamic Speed Guidance
Wenqing Chen

2. Outline
Introduction
Methodology
Case study
Conclusions

3. Introduction-Dilemma Zone
Dilemma zone (DZ) is one of the most contributing factors towards traffic crashes.
The DZs are divided into two categories: Type I DZ and Type II DZ.
When a yellow signal is displayed, a motorist is unable to safely pass the stop line or stop his/her vehicle smoothly before the stop line.

4. Introduction-Dilemma Zone
Current DZ protection is passive, may having some drawbacks: (1) aggressive deceleration; (2) overlong idling time; and (3) drastic speed fluctuation.
With the development of Intelligent Transportation System (ITS), motorists can actively change their driving status reasonably.

5. Introduction-Research Objectives
Develop a dynamic speed guiding method using ITS that can effectively prevent the vehicle from dropping in the DZ while minimizing travel time, speed fluctuation and idling time through the high-signalized intersection.

6. Methodology-Guiding logic and scope
Three main components in the guiding logic:
DZ detection
Dynamic speed guidance
Guidance execution and status tracking
The guiding scope should follow the constraints:
(1) the motorist with the maximum speed limit has enough distance to stop the vehicle, and then accelerate the vehicle back to the maximum speed limit; and, (2) without any congestion, the travel time of vehicle with the median speed for hitting the stop line is no more than the green interval.

7. Methodology-DZ detection
When a vehicle enters the guiding scope, the system shall firstly collect information and then detect if the vehicle will drop in the DZ.
The dynamic guiding model will be activated only if DZ is detected.

8. Methodology-Dynamic speed guiding model
Two modules: (1) DZ protection and travel time minimization; (2) Minimization of speed fluctuation and idling time.
A two-stage model is proposed where Module (1) is processed in Stage I and Module (2) is in Stage II
The Dynamic Programming Algorithm is used to complete Module (1) and the Multi-objectives Mixed Integer Programming Algorithm is used to fulfill Module (2).
The inputs of Module (1) includes initial speed, headway, signal timing; The outputs are speed profile and optimal travel time.
Stage II is conditioning on the output of Stage I.

9. Case study-Selection of study site
Intersection of US 40 (Pulaski Hwy) and Red Toad Road
Pre-design findings are listed in the following table.
Speed Parameter
Unit of mph
Unit of m/s (Integer)
Mean Speed
49.2 22
Median Speed
49.9
Standard Deviation
12.3 5
Minimum Speed
19.6 9
Top Speed
86.7 39
85% Speed
62.4 28

10. Case study-Test design
Based upon the constraints, the DZ guiding scope is set as 400 m.
According to the pre-design findings, the 85% speed is 62.4 mph and the top speed is 86.7 mph, greater than 55 mph, which means some vehicles are overspeed.
Therefore, a deceleration guiding area is added upstream to the DZ guiding area, to ensure the vehicular speed is below 55 mph before the vehicle enters DZ guiding area

11. DZ Protection Strategy Speed Fluctuation Duration (s)
Case study-Result
The results with and without guidance are summarized in the following table.
Scenario Number
TTY (s)
DZ Protection Strategy
Travel Time (s)
Idling Time (s)
Speed Fluctuation Duration (s)
With
Guidance
Without Guidance
With Guidance 1
(Maximum Speed) 10
Deceleration
All-red Extension 30 17 14 2
(Median speed) 19 3
(50% Max Speed) 26
Acceleration 20 34 12 4
(Minimum Speed) 38 22 45 15
It can be found that with the dynamic speed guidance, the vehicle can avoid the DZ without all-red extension. For Scenarios 3 and 4, the travel time with guidance is shorter than without guidance, as the vehicle can accelerate to pass the stop line. In addition, due to the extremely short red interval, there’s no idling time in all scenarios.

12. Case study-Trajectory analysis
The vehicle under all scenarios could avoid DZ with guidance.
When the initial speed is below the maximum speed limit, the travel time with guidance is lower than without guidance.
When the initial speed is equal to the maximum speed limit, the travel time with and without guidance equal, while the idling time with guidance is lower than without guidance.

13. Case study-Sensitivity analysis
When the initial speed is close to the maximum speed limit, the travel time almost maintains the same under various scope guiding area. While if the initial speed is much lower than the maximum speed limit, the travel time rises with the increase of guiding scope.
When the initial speed is much lower than the maximum speed limit, the speed fluctuation duration remains the same under various scope guiding area. While if the initial speed is close to the maximum speed limit, the speed fluctuation declines with the increase of guiding scope.
The sensitivity analysis implies that if most vehicles has high speed, the guiding scope can be set longer. Otherwise, a shorter guiding scope may be appropriate.

14. Conclusions
This paper proposes a dynamic speed guiding model towards DZ protection through high-speed signalized intersection. The conclusions are summarized as follows:
For higher initial speed, motorists can decelerate to pass the stop line without idling. While for the lower initial speed, acceleration is applicable for the motorists to pass the intersection safely, quickly and comfortably.
A case study indicates that Compared with the situation without control, vehicle with the control algorithm can avoid DZ and passes the intersection without idling.
The results indicate that the travel time of high speed almost maintains the same under various scope guiding area. While the travel time of low speed the travel time rises with the increase of guiding scope. For the speed fluctuation duration, the low speed seems stable while the high speed reflects a rising trend with the increase of the guiding scope.
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