Designing Sustainable Public Transportation: Integrated Optimization of Bus Speed and Holding Time in a Connected Vehicle Environment
Abstract
:1. Introduction
- Explicitly capture the dynamic interaction between bus acceleration, speed, and holding time;
- Optimize bus speed and holding time of buses dynamically in an united framework;
- Satisfy the objectives of both improving driving patterns of buses and minimizing the bus delay, fuel consumption, and pollution emissions, which is conducive for city sustainability.
2. Development of the Optimization Model
2.1. Problem Description
2.2. General Notations
2.3. Objective Function
2.4. Decision Variables
- (1)
- Holding time at bus stop, .
- (2)
- Bus traveling speed, .
2.5. Constraints
- Scenario A, when or (including A1 and A2);
- Scenario B, when ;
- Scenario C, when ;
- Scenario D, when .
2.5.1. Scenario A
2.5.2. Scenario B
2.5.3. Scenario C
2.5.4. Scenario D
2.5.5. Optimization of the Proposed Method
- Step 1: Given the cycle time, traffic demands, and the location of the bus stop, compute the green time duration, the maximum green extension time, and the time boundary points for each scenario.
- Step 2: If the bus arrival time is not located in scenario A, then turn to step 3. Otherwise, compute the time point at which the bus stopped by the red light and the time point at which the bus started to move by the green light. Then compute the bus signal delay caused by the red light, the queue, and the bus acceleration cost.
- Step 3: If the bus arrival time is not located in scenario B, then turn to step 4. Otherwise, compute the bus holding time and bus travel speed, then compute the bus holding delay, travel delay, and the bus acceleration cost.
- Step 4: If the bus arrival time is not located in scenario C, then turn to step 5. Otherwise, compute the optimal bus travel speed, and then compute the bus travel delay and the bus acceleration cost.
- Step 5: Compute the bus travelling delay and bus acceleration cost in scenario D.
3. Results and Discussion
3.1. Performance Analysis
- Case 1: Traditional control method with neither holding nor speed control;
- Case 2: Speed control only;
- Case 3: Holding control only;
- Case 4: The proposed control method including both holding and speed control.
3.2. SimulationTest
3.3. Sensitivity Analysis
3.3.1. Sensitivity Analysis with Degree of Saturation
3.3.2. Sensitivity Analysis with Bus Stop Location
3.3.3. Sensitivity Analysis with Maximum Speed Limits
4. Strengths and Limitations
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Key Variables | Definition |
---|---|
, | The maximum and minimum accelerations forbuses (m/s2) |
Cycle length of the signal timing (s) | |
Bus delay cost (s) | |
Bus holding delay (s) | |
Bus signal delay (s) | |
Bus travel delay (s) | |
The distance from bus stop to the intersection (m) | |
The maximum queue length (m) | |
The average vehicle length (m) | |
Arrival flow rate (# of vehs/s) | |
Saturation flow rate (# of vehs/s) | |
Time for buses ready to depart from bus stop (s) | |
Time for green light starts (s) | |
Time for buses join in the queue (s) | |
Time for queue dissipated (s) | |
Time for buses clearing the intersection (s) | |
, , , | The boundary point for scenario A, B, C and D (s) |
Time duration for holding the bus at bus stop (s) | |
Time duration for a bus accelerates from zero to bus traveling speed (s) | |
Bus traveling speed (m/s) | |
, | The maximum and minimum bus speed limits (m/s) |
Scenario | Average Bus Delay Cost (Average Acceleration Cost) | |||
---|---|---|---|---|
Case 1 | Case 2 | Case 3 | Case 4 | |
Scenario A (−24.9, 7.3) | 30.5 (33.3) | 30.5 (33.3) | 30.5 (33.3) | 30.5 (33.3) |
Scenario B [7.3, 22.3) | 16.9 (33.3) | 18.7 (31.3) | 16.9 (33.3) | 26.1 (11.1) |
Scenario C [22.3, 36.0) | 8.8 (33.3) | 10.2 (11.1) | 10.2 (11.1) | 10.2 (11.1) |
Scenario D [36.0, 50.1] | 1.85 (11.1) | 1.85 (11.1) | 1.85 (11.1) | 1.85 (11.1) |
Cases | |||
---|---|---|---|
Case 1 | [36.0, 50.1] | 14.1 | 20.1% |
Case 2 | [21.0, 50.1] | 29.1 | 41.6% |
Case 3 | [22.3, 50.1] | 27.8 | 39.7% |
Case 4 | [7.3, 50.1] | 42.8 | 61.1% |
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Wu, W.; Ma, W.; Long, K.; Zhou, H.; Zhang, Y. Designing Sustainable Public Transportation: Integrated Optimization of Bus Speed and Holding Time in a Connected Vehicle Environment. Sustainability 2016, 8, 1170. https://doi.org/10.3390/su8111170
Wu W, Ma W, Long K, Zhou H, Zhang Y. Designing Sustainable Public Transportation: Integrated Optimization of Bus Speed and Holding Time in a Connected Vehicle Environment. Sustainability. 2016; 8(11):1170. https://doi.org/10.3390/su8111170
Chicago/Turabian StyleWu, Wei, Wanjing Ma, Kejun Long, Heping Zhou, and Yi Zhang. 2016. "Designing Sustainable Public Transportation: Integrated Optimization of Bus Speed and Holding Time in a Connected Vehicle Environment" Sustainability 8, no. 11: 1170. https://doi.org/10.3390/su8111170
APA StyleWu, W., Ma, W., Long, K., Zhou, H., & Zhang, Y. (2016). Designing Sustainable Public Transportation: Integrated Optimization of Bus Speed and Holding Time in a Connected Vehicle Environment. Sustainability, 8(11), 1170. https://doi.org/10.3390/su8111170