# Developing and Field Testing a Green Light Optimal Speed Advisory System for Buses

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. B-GLOSA System

_{up}to the downstream location d

_{down}. It should be noted that both d

_{up}and d

_{down}are computed based on the distance to the intersection stop bar. Here, the intersection downstream location d

_{down}is defined to ensure that buses that passed through intersections with low speeds have enough distance to accelerate to the roadway speed limit, if the downstream traffic condition is uncongested. A bus generally has two options to approach a signalized intersection: (1) deceleration is needed; (2) deceleration is not needed. Therefore, the GLOSA algorithms for these two options are developed in this section. More detailed discussions of the options for vehicle to pass signalized intersections are presented in [26,27].

_{up}) or accelerate to a speed u

_{c}and then keep driving with that constant speed to pass the intersection. The cruise speed is calculated in Equation (1). Here, t

_{r}denotes the remaining red indication time when vehicle arrives d

_{up}upstream of the intersection. If the initial vehicle speed is equal to u

_{c}, the vehicle can use the same initial speed to pass the intersection. Otherwise, the vehicle needs to follow the bus engine physical model–vehicle dynamics model denoted in Equations (2)–(4) and accelerate to the speed u

_{c}to pass the intersection. Here, a vehicle dynamics model developed in [28] is used to capture the behavior of the acceleration maneuver.

_{p}represents the throttle level ranging between 0 and 1; η

_{d}denotes the efficiency of the driveline; m

_{ta}represents the mass along the tractive axle (kilogram); P denotes the power of engine (kilowatt); μ is the road adhesion coefficient parameter; g represents the gravitational acceleration value (9.8067 m per second

^{2}); ρ denotes the air density under a temperature of 15 °C and sea level (1.2256 kg per meter

^{3}); C

_{h}represents the correction factor of altitude; C

_{d}denotes the coefficient of vehicle drag; m represents the vehicle mass (kilogram); and G denotes the grade of roadway; A

_{f}represents the frontal area of vehicle (meter

^{2}); c

_{r}

_{0}, c

_{r}

_{1}and c

_{r}

_{2}denote the rolling resistance constant values.

_{up}, with a speed of u (t

_{0}), the vehicle needs to reduce the speed to u

_{c}by following the decelerate level of a, and then the vehicle maintains the cruise speed of u

_{c}to approach the intersection. When this vehicle drives on the downstream road of the intersection, the vehicle needs to speed up from the cruise speed to u

_{f}, and then maintain this speed to pass the location d

_{down}. The fuel-optimized vehicle trajectory can be computed by solving the optimization problem as below. It should be noted that this optimization problem only has two unknown variables—the vehicle deceleration a and the throttle input f

_{p}.

_{up}) at the time of t

_{0}, and then passes the downstream location (d

_{down}) at the time of t

_{0}+ T. The intersection upstream cruise speed is u

_{c}. The objective function entails minimizing the total fuel consumption level as:

_{min}and a

_{max}denote the minimum and maximum allowed acceleration levels to ensure driving comfort, and f

_{min}and f

_{max}represent the minimum and maximum throttle levels. According to the relationships in Equations (5)–(7), the deceleration a and throttle level f

_{p}are the only unknown variables. A moving-horizon dynamic programming approach is implemented here to find the optimal solution of the optimization problem. In this way, all the combinations of deceleration and throttle levels are enumerated and the corresponding trip fuel consumption levels from upstream location d

_{up}to downstream location d

_{down}are computed. Therefore, the optimum parameters can be located according to the minimum fuel consumption level [13,27]. Considering that the optimization solution needs to be calculated at a rapid frequency (e.g., 10 Hz) for real-time applications, an A-star algorithm is used here to expedite the computation speed to achieve real-time computations [20]. The deceleration speed and the throttle level are considered as constant values in the A-star algorithm. Considering that the proposed system will be used to compute optimal trajectory for buses in real time, the computation speed and efficiency is critical in selecting the A-star algorithm. Compared to other pathfinding algorithms, such as Dijkstra’s algorithm, which explores all possible paths, the A-star algorithm adds a heuristic to the cost function to improve the computational efficiency and speed [29]. In order to solve the proposed optimization problem, we firstly assume the throttle level is a constant value (e.g., 0.6), and then the optimal deceleration level can be computed, which corresponds to the minimal energy consumption for the upstream and downstream roadway of the intersection. Therefore, the starting speed (vehicle speed when traversing the stop-bar) and the ending speed (roadway speed limit) during the downstream roadway are known, and eventually the optimal throttle level can be located according to the minimal energy consumption for the downstream trip. Given that the optimal solution is recalculated at a temporal interval of 0.1 s, the acceleration/deceleration and throttle levels are also updated every 0.1 s.

#### 2.2. GLOSA for Buses

## 3. Case Study

#### 3.1. Test Environment

_{up}and d

_{down}are equal to 200 m. During the test drive in the uphill direction, the bus can accelerate up to 32–34 mph before merging to turnaround 1 if the bus was fully stopped at the intersection. Therefore, the speed limit was set as 30 mph. In order to have a fair comparison across different runs, buses attempted to drive at 30 mph before entering and after leaving the control range. Thus, two cones were placed at 200 m upstream (the first cone) and 200 m downstream (the second cone) of the intersection in each direction; thus, in total there were four cones, past which drivers were asked to drive at 30 mph.

_{up}, the countdown of the red offset (the remaining red indication time) is triggered by a random value from 10, 15, 20 or 25 s. Moreover, the upcoming green indication time is set as 25 s to ensure the bus can arrive at the downstream location, even if the bus is completely stopped at the signalized intersection.

_{up}to the downstream location d

_{down}. Eventually, 1440 sets of trip information were collected as the raw dataset to analyze the system performance in the field test.

**Scenario 1 (S1)—Uninformed drive:**

**Scenario 2 (S2)—Informed drive with the provision of signal timing information:**

**Scenario 3 (S3)—Informed drive with recommended speed (B-GLOSA):**

#### 3.2. Experimental Design and Statistical Analysis

#### 3.3. Quantitative Performance Analysis

## 4. Conclusions

- A fuel consumption model for diesel buses was used in the proposed system to compute instantaneous fuel consumption rates, because this model is easy to calibrate using easy-to-access bus data.
- The vehicle dynamics model, fuel consumption model, signal timings, and vehicle speed and distance relationship are used to construct an optimization problem.
- A moving-horizon dynamic program and an A-star algorithm is used to solve the optimization problem and calculate the energy-optimized vehicle trajectory to assist buses to proceed through signalized intersections efficiently. The proposed B-GLOSA system was implemented and field tested to validate the real-world benefits. The test results and the recommendations for future research are summarized below.
- The Virginia Smart Road test facility was used to conduct the field test using 30 participants. A split-split-plot experimental design was used to test the developed B-GLOSA system for different impact factors of road grades and red indication offsets, and statistical analysis was conducted to demonstrate that the fuel consumption performances were significantly different among three test scenarios.
- The quantitative analysis of the test results demonstrated that the proposed B-GLOSA system can greatly smooth the bus trajectory while traversing a signalized intersection, and simultaneously save fuel consumption and travel times.
- Compared to the uninformed drive, the test results demonstrated that the B-GLOSA can efficiently reduce fuel consumption by 22.1% and simultaneously reduce vehicle travel times by 6.1%.
- In future research, the B-GLOSA system will be tested within a microscopic simulation environment to quantify he network-level impact for various traffic conditions and heterogeneous traffic including LDVs and buses.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**Comparison of test results for fuel levels and travel times: (

**a**) fuel in downhill; (

**b**) travel time in downhill; (

**c**) fuel in uphill; (

**d**) travel time in uphill.

**Figure 7.**Vehicle speed profiles of a selected participant for the downhill direction under various red offset timings: (

**a**) 10 s; (

**b**) 15 s; (

**c**) 20 s; (

**d**) 25 s.

Response Variable | Source | DF | DFDen | F Ratio | p Value |
---|---|---|---|---|---|

Fuel Consumption | Scenario | 2 | 146 | 83.004 | <0.0001 |

Red offset | 3 | 1255 | 1182.769 | <0.0001 | |

Grade | 1 | 175 | 7355.448 | <0.0001 | |

Scenario*Grade | 2 | 175 | 10.658 | 0.1872 | |

Scenario*Red offset | 6 | 1255 | 12.449 | 0.0685 | |

Red offset*Grade | 3 | 1255 | 30.084 | <0.0001 | |

Scenario*Red offset*Grade | 6 | 1255 | 8.796 | 0.1236 | |

Travel Time | Scenario | 2 | 146 | 660.503 | <0.0001 |

Red offset | 3 | 1255 | 8623.917 | <0.0001 | |

Grade | 1 | 175 | 131.278 | 0.0853 | |

Scenario*Grade | 2 | 175 | 13.477 | 0.0762 | |

Scenario*Red offset | 6 | 1255 | 53.352 | 0.1082 | |

Red offset*Grade | 3 | 1255 | 0.900 | 0.4849 | |

Scenario*Red offset*Grade | 6 | 1255 | 3.029 | 0.6215 |

Direction | Red Offset (Sec) | Scenario 1 FC (Liter) | Scenario 2 FC (Liter) | Scenario 3 FC (Liter) | Difference between S2 and S1 (%) | Difference between S3 and S1 (%) |
---|---|---|---|---|---|---|

Downhill | 10 | 0.102 | 0.072 | 0.056 | −29.7% | −44.9% |

15 | 0.179 | 0.151 | 0.091 | −15.3% | −49.1% | |

20 | 0.217 | 0.202 | 0.161 | −6.7% | −25.8% | |

25 | 0.229 | 0.224 | 0.190 | −2.1% | −16.8% | |

Uphill | 10 | 0.369 | 0.356 | 0.354 | −3.5% | −4.2% |

15 | 0.424 | 0.390 | 0.360 | −8.0% | −15.1% | |

20 | 0.451 | 0.419 | 0.399 | −7.1% | −11.6% | |

25 | 0.462 | 0.438 | 0.419 | −5.3% | −9.3% | |

Downhill Average | 0.182 | 0.162 | 0.125 | −13.4% | −34.2% | |

Uphill Average | 0.427 | 0.401 | 0.383 | −6.0% | −10.1% | |

Total Average | 0.304 | 0.282 | 0.254 | −9.7% | −22.1% |

Direction | Red Offset (Sec) | Scenario 1 TT (Sec) | Scenario 2 TT (Sec) | Scenario 3 TT (Sec) | Difference between S2 and S1 (%) | Difference between S3 and S1 (%) |
---|---|---|---|---|---|---|

Downhill | 10 | 30.4 | 29.6 | 29.4 | −2.9% | −3.3% |

15 | 34.1 | 33.1 | 30.6 | −2.8% | −10.1% | |

20 | 40.1 | 39.0 | 36.7 | −2.9% | −8.5% | |

25 | 45.7 | 45.1 | 43.1 | −1.4% | −5.6% | |

Uphill | 10 | 31.1 | 30.2 | 30.0 | −2.9% | −3.5% |

15 | 35.5 | 34.3 | 32.0 | −3.3% | −9.7% | |

20 | 42.0 | 40.3 | 39.9 | −3.9% | −5.0% | |

25 | 47.3 | 46.4 | 46.0 | −2.0% | −2.7% | |

Downhill Average | 37.6 | 36.7 | 35.0 | −2.5% | −6.9% | |

Uphill Average | 39.0 | 37.8 | 37.0 | −3.0% | −5.3% | |

Total Average | 38.3 | 37.2 | 36.0 | −2.8% | −6.1% |

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**MDPI and ACS Style**

Chen, H.; Rakha, H.A. Developing and Field Testing a Green Light Optimal Speed Advisory System for Buses. *Energies* **2022**, *15*, 1491.
https://doi.org/10.3390/en15041491

**AMA Style**

Chen H, Rakha HA. Developing and Field Testing a Green Light Optimal Speed Advisory System for Buses. *Energies*. 2022; 15(4):1491.
https://doi.org/10.3390/en15041491

**Chicago/Turabian Style**

Chen, Hao, and Hesham A. Rakha. 2022. "Developing and Field Testing a Green Light Optimal Speed Advisory System for Buses" *Energies* 15, no. 4: 1491.
https://doi.org/10.3390/en15041491