A Ridesharing Choice Behavioral Equilibrium Model with Users of Heterogeneous Values of Time
Abstract
:1. Introduction
2. Literature Review
3. Model Formulation
3.1. Assumptions
- Travelers/users are heterogeneous in terms of their VOTs and can be categorized into finite number of classes according to their VOTs.
- Each traveler owns a vehicle, and they each choose one of the three travel modes to complete his/her trips, i.e., solo driver(s) (SDs), ridesharing driver(s) (RDs), and ridesharing passenger(s) (RPs).
- Each RP takes a ride from only one RD, however each RD may pick up more than one RPs from the same OD pair. The RP’s OD pair may be different from the matched RD’s OD pair.
- The vehicles are uniform, and the vehicle capacity is limited and predetermined.
3.2. Model Description
3.3. Cost Functions
3.3.1. Congestion Cost (Travel Time)
3.3.2. Driving Cost
3.3.3. Inconvenience Cost
3.3.4. Compensations of RDs and Ridesharing Fees of RPs
3.3.5. Path Cost Function
3.4. Nonlinear Complementarity Formulation
4. The Equivalent Variational Inequality Formulation and Existence of the Model Solution
5. Numerical Experiments
5.1. Computational Result
5.2. Sensitivity Analysis
5.3. The Impact of VOTs on Ridesharing
5.4. The Impact of HOT Lane on Ridesharing
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
Abbreviations
N | the set of nodes |
A | the set of links, whose index is |
W | the set of OD pairs, whose index is |
the set of routs of OD pair | |
R | the set of routs of all OD pairs |
number of travelers choosing mode i in class m on link a where | |
m | a typical user class,,M denotes the number of such traveler classes |
1, if link on path and 0, otherwise | |
vehicle capacity | |
travel time on link | |
, | multipliers for ride-matching constraints |
a parameter for ridesharing passenger in class m to reflect the intolerance to congestion time | |
, | parameters of inconvenience cost for ridesharing driver and ridesharing passenger, respectively |
, | parameters of compensation and payment for ridesharing driver and ridesharing passenger, respectively |
number of links where RDs travel with RPs | |
guiding price for taking rides or for charging compensation | |
, | A simplified representation of the inconvenience cost functionsfor ridesharing driver and ridesharing passenger, respectively |
, | A simplified representation of the compensation function and the payment function for RD and RP, respectively |
, | the normal travel cost function and the generalized cost function for solo driver in class m on path r |
, | the normal travel cost function and the generalized cost function for ridesharing driver in class m on path r who travels with ridesharing passenger on path s |
, | the normal travel cost function and the generalized cost function for ridesharing passenger in class m on path r who shares ride with ridesharing driver on path p |
travel demand of class m between OD pair w | |
the minimum generalized path cost for traveler in class m between OD pair w | |
the average VOT for travelers of class m | |
n | parameters related to driving cost |
price of fuel per unit |
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OD Pair | OD Pair | |||||
---|---|---|---|---|---|---|
Path 1-3-2 | Path 1-4-2 | Path 3-2 | ||||
R1 | (1-3,3-2) | R7 | (1-4,4-2) | R13 | (3-2) | |
R2 | (1-3,3-2) | R8 | (1-4,4-2) | R14 | (3-2) | |
R3 | (1-3,3-2) | R9 | (1-4,4-2) | R15 | (3-2) | |
R4 | (1-3,3-2) | R10 | (1-4,4-2) | R16 | (3-2) | |
R5 | (1-3,3-2) | R11 | (1-4,4-2) | R17 | (3-2) | |
R6 | (1-3,3-2) | R12 | (1-4,4-2) | R18 | (3-2) | |
R19 | (1-3, 3-2) | R21 | (3-2) | |||
R20 | (1-3, 3-2) | R22 | (3-2) |
OD Pair 1 | OD Pair 2 | |||||||
---|---|---|---|---|---|---|---|---|
Path 1-3-2 | Path 1-4-2 | Path 3-2 | ||||||
Extended Route | Route Flow | Generalized Cost | Extended Route | Route Flow | Generalized Cost | Extended Route | Route Flow | Generalized Cost |
R1 | 0.00 | 89.9127 | R7 | 0.00 | 89.9402 | R13 | 0.00 | 56.7126 |
R2 | 14.01 | 88.6829 | R8 | 31.56 | 88.6829 | R14 | 8.66 | 55.9623 |
R3 | 7.67 | 88.6248 | R9 | 7.71 | 88.6248 | R15 | 0.00 | 55.4247 |
R4 | 0.00 | 89.6232 | R10 | 0.00 | 89.6099 | R16 | 8.27 | 55.9623 |
R5 | 15.35 | 88.6248 | R11 | 15.43 | 88.6248 | R17 | 14.64 | 54.1837 |
R6 | 0.00 | 91.2948 | R12 | 0.00 | 91.2782 | R18 | 1.90 | 55.9623 |
R19 | 7.60 | 88.6247 | R21 | 12.24 | 54.1837 | |||
R20 | 0.67 | 88.6829 | R22 | 4.29 | 55.9623 |
1.00 | 1.05 | 1.10 | 1.15 | 1.20 | 1.25 | 1.30 | 1.35 | 1.40 | 1.45 | 1.50 | |
2.73 | 2.87 | 3.02 | 3.17 | 3.34 | 3.51 | 3.69 | 3.87 | 4.06 | 4.23 | 4.38 | |
- | - | - | - | - | - | - | 5.16 | 5.19 | 5.22 | 5.27 | |
1.55 | 1.60 | 1.65 | 1.70 | 1.75 | 1.80 | 1.85 | 1.90 | 1.95 | 2.00 | ||
4.51 | 4.61 | 4.68 | 4.74 | 4.78 | 4.81 | 4.84 | - | - | - | ||
5.32 | 5.40 | 5.52 | 5.67 | 5.87 | 6.12 | 6.40 | 6.72 | 7.06 | 7.43 |
OD Pair 1 | OD Pair 2 | ||||
---|---|---|---|---|---|
Path 1-3-2 | Path 1-4-2 | Path 3-2 | |||
R1 | (1-3,3-2) | R7 | (1-4,4-2) | R13 | (3-2) |
R2 | (1-3,3-2) | R8 | (1-4,4-2) | R14 | (3-2) |
R3 | (1-3,3-2) | R9 | (1-4,4-2) | R15 | (3-2) |
R4 | (1-3,3-2) | R10 | (1-4,4-2) | R16 | (3-2) |
R5 | (1-3,3-2) | R11 | (1-4,4-2) | R17 | (3-2) |
R6 | (1-3,3-2) | R12 | (1-4,4-2) | R18 | (3-2) |
R19 | (1-3,3-2) | R21 | (3-2) | ||
R20 | (1-3,3-2) | R22 | (3-2) | ||
R23 | (1-3,3-2) | R29 | (3-2) | ||
R24 | (1-3,3-2) | R30 | (3-2) | ||
R25 | (1-3,3-2) | R31 | (3-2) | ||
R26 | (1-3,3-2) | R32 | (3-2) | ||
R27 | (1-3,3-2) | R33 | (3-2) | ||
R28 | (1-3,3-2) | R34 | (3-2) | ||
R35 | (1-3,3-2) | R37 | (3-2) | ||
R36 | (1-3,3-2) | R38 | (3-2) |
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Li, X.; Bai, J. A Ridesharing Choice Behavioral Equilibrium Model with Users of Heterogeneous Values of Time. Int. J. Environ. Res. Public Health 2021, 18, 1197. https://doi.org/10.3390/ijerph18031197
Li X, Bai J. A Ridesharing Choice Behavioral Equilibrium Model with Users of Heterogeneous Values of Time. International Journal of Environmental Research and Public Health. 2021; 18(3):1197. https://doi.org/10.3390/ijerph18031197
Chicago/Turabian StyleLi, Xingyuan, and Jing Bai. 2021. "A Ridesharing Choice Behavioral Equilibrium Model with Users of Heterogeneous Values of Time" International Journal of Environmental Research and Public Health 18, no. 3: 1197. https://doi.org/10.3390/ijerph18031197