A Framework to Determine the Utilization of Vacant Taxis on HOV Lanes with the Optimal Deployment
Abstract
:1. Introduction
2. Preliminaries
- the demand between OD pair
- the demand for travel mode between OD pair
- the demand for vacant taxis between OD pair
- the value of time of travelers
- the value of waiting time of taxi passengers
- the area of origin
- the length of link
- the capacity of link
- the operation cost per unit distance of solo-driving travelers
- the flag–fall price per ride
- the mileage-based fare per ride
- the delay-based fare per ride
- the operation cost per unit distance of vacant taxis
- travel time function on link , which is strictly increasing, convex, and continuous with the flow on link
- A binary constant that equals 1 when link is on the path between OD pair and 0 otherwise.
- the flow of travel mode on path between OD pair
- the flow of vacant taxis on path between OD pair
- the vehicle flow on link
- the vehicle flow of mode on link
- the vehicle flow of vacant taxis on link
3. Formulations
3.1. Cost Functions
3.2. Model Constraints
3.3. Travel Mode Split and Path Choice
3.4. Varational Inequality
4. The Network Performance
5. Optimal Deployment of HOV Lanes
6. Algorithm
7. Numerical Examples
7.1. Simple Network Example
7.2. Sioux Falls Network Example
8. Conclusions
- (1)
- A paradox similar to the Braess paradox is revealed. Given HOV lane deployment, allowing vacant taxis to use HOV lanes may be negative for maximization of social welfare with intensive usage of HOV lanes. This paradox may derive from the congestion in GP lanes and the capacity limits of the bottlenecks, instead of the congestion in HOV lanes. Allowing vacant taxis to use HOV lanes can intensify the utilization of the HOV lanes while decreasing social welfare.
- (2)
- Considering optimization of HOV lane deployment, allowing vacant taxis to use HOV lanes is more likely negative to social welfare due to the paradox, although the optimal deployments are different in two cases.
- (3)
- The paradox depends on the topology and the parameters of the network, e.g., the flag–fall price of taxis. If the paradox is inexistent, the scheme may be beneficial to the traffic system. Therefore, specific information and analysis are necessary to determine whether to forbid or allow vacant taxis to use HOV lanes.
- (4)
- The models and the algorithms can be used in reality.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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D | 1 | 2 | 3 | 4 | 5 | 6 | |
---|---|---|---|---|---|---|---|
O | |||||||
1 | 0 | 600 | 800 | 600 | 600 | 600 | |
2 | 600 | 0 | 600 | 600 | 600 | 600 | |
3 | 800 | 600 | 0 | 600 | 800 | 600 | |
4 | 600 | 600 | 600 | 0 | 600 | 600 | |
5 | 800 | 600 | 800 | 600 | 0 | 600 | |
6 | 600 | 600 | 800 | 600 | 600 | 0 |
Link | (h) | (veh/h) | (km) | Link | (h) | (veh/h) |
---|---|---|---|---|---|---|
1-2(GP) | 0.03 | 2400 | 2.1 | 4-2(GP) | 0.02 | 3600 |
2-1(GP) | 0.03 | 2400 | 2.1 | 3-5(GP) | 0.03 | 2400 |
1-3(GP) | 0.03 | 2400 | 2.1 | 5-3(GP) | 0.03 | 2400 |
3-1(GP) | 0.03 | 2400 | 2.1 | 5-6(GP) | 0.04 | 2400 |
3-4(GP) | 0.04 | 2400 | 2.8 | 6-5(GP) | 0.04 | 2400 |
4-3(GP) | 0.04 | 2000 | 2.8 | 4-6(GP) | 0.04 | 2400 |
2-4(GP) | 0.02 | 3600 | 1.4 | 6-4(GP) | 0.04 | 2400 |
1-2(HOV) | 0.03 | 600 | 2.1 | 4-2(HOV) | 0.02 | 900 |
2-1(HOV) | 0.03 | 600 | 2.1 | 3-5(HOV) | 0.03 | 600 |
1-3(HOV) | 0.03 | 600 | 2.1 | 5-3(HOV) | 0.03 | 600 |
3-1(HOV) | 0.03 | 600 | 2.1 | 5-6(HOV) | 0.04 | 600 |
3-4(HOV) | 0.04 | 600 | 2.8 | 6-5(HOV) | 0.04 | 600 |
4-3(HOV) | 0.04 | 500 | 2.8 | 4-6(HOV) | 0.04 | 600 |
2-4(HOV) | 0.02 | 900 | 1.4 | 6-4(HOV) | 0.04 | 600 |
Social Welfare | Solo-Driving Demand | Carpooling Demand | Occupied Taxi Demand | |
---|---|---|---|---|
Case 1 | 413,638 | 11,849 | 909 | 1399 |
Case 2 | 421,983 | 11,808 | 939 | 1443 |
Social Welfare | Solo-Driving Demand | Carpooling Demand | Occupancy Taxi Demand | |
---|---|---|---|---|
Case 1 | 160,739 | 6822 | 189 | 3030 |
Case 2 | 162,542 | 6820 | 188 | 3036 |
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Gao, F.; Liu, K.; Ding, D. A Framework to Determine the Utilization of Vacant Taxis on HOV Lanes with the Optimal Deployment. Appl. Sci. 2023, 13, 913. https://doi.org/10.3390/app13020913
Gao F, Liu K, Ding D. A Framework to Determine the Utilization of Vacant Taxis on HOV Lanes with the Optimal Deployment. Applied Sciences. 2023; 13(2):913. https://doi.org/10.3390/app13020913
Chicago/Turabian StyleGao, Fawen, Kun Liu, and Dong Ding. 2023. "A Framework to Determine the Utilization of Vacant Taxis on HOV Lanes with the Optimal Deployment" Applied Sciences 13, no. 2: 913. https://doi.org/10.3390/app13020913
APA StyleGao, F., Liu, K., & Ding, D. (2023). A Framework to Determine the Utilization of Vacant Taxis on HOV Lanes with the Optimal Deployment. Applied Sciences, 13(2), 913. https://doi.org/10.3390/app13020913