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A Framework to Integrate Mode Choice in the Design of Mobility-on-Demand Systems
Yang Liu, Prateek Bansal, Ricardo Daziano, Samitha Samaranayake
TL;DR
Fixed-demand MoD models do not capture how travelers choose among competing modes or address broader transportation-system effects. The paper integrates mode choice with MoD operations and uses Bayesian optimization to tune supply parameters; numerical experiments show convergence and better performance than random search, while a ride-hailing tax scenario illustrates policy effects.
Problem
Fixed-demand MoD models assume demand rather than accounting for mode choice, limiting analysis of effects on transit ridership and other system-level outcomes.
Source: §1 · p. 2Method
The paper combines a multimodal mode-choice model with MoD operations and applies Bayesian optimization to optimize supply-side parameters.
Source: §1 · p. 3, §5 · p. 25Results
Numerical experiments show convergence of the integrated supply-demand system, and the Bayesian-optimization approach outperforms traditional random search.
Source: §5 · p. 26Takeaways & Limitations
A ride-hailing tax scenario shows increased transit ridership, reduced MoD vehicle miles traveled, and reduced provider profit when higher-capacity services require higher discounts.
Source: §5 · p. 26The model considers a single MoD operator and does not address competition between providers.
Source: §1 · p. 4
Abstract
from arXiv · showhide
Mobility-on-Demand (MoD) systems are generally designed and analyzed for a fixed and exogenous demand, but such frameworks fail to answer questions about the impact of these services on the urban transportation system, such as the effect of induced demand and the implications for transit ridership. In this study, we propose a unified framework to design, optimize and analyze MoD operations within a multimodal transportation system where the demand for a travel mode is a function of its level of service. An application of Bayesian optimization (BO) to derive the optimal supply-side MoD parameters (e.g., fleet size and fare) is also illustrated. The proposed framework is calibrated using the taxi demand data in Manhattan, New York. Travel demand is served by public transit and MoD services of varying passenger capacities (1, 4 and 10), and passengers are predicted to choose travel modes according to a mode choice model. This choice model is estimated using stated preference data collected in New York City. The convergence of the multimodal supply-demand system and the superiority of the BO-based optimization method over earlier approaches are established through numerical experiments. We finally consider a policy intervention where the government imposes a tax on the ride-hailing service and illustrate how the proposed framework can quantify the pros and cons of such policies for different stakeholders.
1. Introduction
The introduction argues that fixed-demand MoD design cannot capture how travelers choose among competing modes or answer broader system-level policy questions. It presents a multimodal framework that integrates mode choice with MoD operations and uses Bayesian optimization to tune supply-side parameters.
Motivation and research gap
- Fixed-demand models assume travelers who can be served by MoD will choose it, although choices also depend on competing modes and individual preferences.This limits their ability to address system-level questions such as effects on transit ridership, vehicle ownership, and parking demand.Source: §1 · pp. 2–3
Optimization contribution
- Unlike prior supply-demand studies focused on policy sensitivity, this work targets optimal supply-side choices, using Bayesian optimization to search the transportation simulation as a black box.The approach decouples supply-parameter optimization from the vehicle assignment problem.Source: §1 · pp. 3–4
Framework contribution
- The framework combines mode choice with real-time MoD fleet management for ride-hailing, ridepooling, micro-transit, and public transit, calibrated with New York City stated-preference data.The Manhattan application models MoD capacities of 1, 4, and 10 passengers under a single provider.Source: §1 · p. 3
Scope and intended use
- The framework is intended to help analyze MoD effects on urban mobility and system-level policy questions while tuning supply parameters that influence demand.The introduction identifies government intervention and transit ridership as examples of such questions.Source: §1 · pp. 3–4
Limitation
- The model considers one MoD operator and does not represent competition between providers, although MoD and taxi services can coexist.Integrating competitive behavior and the resulting market equilibrium is left for future research.Source: §1 · p. 4
2. Framework: Modeling Mobility-on-Demand Systems within a Multimodal Transportation System
The framework links mode choice to transit and MoD operations, then uses Bayesian optimization to tune supply parameters against an objective evaluated at inner-loop equilibrium. It models evolving mode choices using historical service attributes.
2. Framework: Modeling Mobility-on-Demand Systems within a Multimodal Transportation System
- An outer Bayesian-optimization loop evaluates supply parameters at inner-loop equilibrium, where mode shares and service attributes are iteratively updated until choices stabilize.The objective can represent system-level measures such as operator profit or consumer surplus.Source: §2 · pp. 4–5
2.1. Mode Choice Model and Data
- A stated-preference experiment with 1,507 valid respondents estimated an MNL for Uber, UberPool, and current mode; nested-logit specifications exceeded accepted correlation bounds.MNL probabilities feed the simulation; the main study was conducted in October–November 2017.Source: §2.1 · pp. 6–7, §2.2 · p. 7
2.2.1. Simulation of the MoD system
- Vehicles are assigned to feasible trips by a 60-second ILP that minimizes delay with a penalty for unassigned requests, followed by idle-vehicle rebalancing.The assignment simulator retains requests until their maximum waiting-time constraint is violated.Source: §2.2.1 · pp. 9–10
2.2.2. Simulation of the Public Transit Service
- Transit service attributes are computed from a GTFS-based network combined with the road network, using walk-transit-walk shortest paths for each origin-destination pair.The combined-network link costs include walking time, expected wait, and transit fare converted to seconds.Source: §2.2.2 · p. 11
2.3. Updating Historical Trip Attributes and Inner Loop Stopping Criterion
- Clustered historical attributes feed next-round choices; unsatisfied MoD demand shifts to transit with a utility penalty, and iterations stop when mean mode-share change falls below 0.01.Historical attributes include in-vehicle time, waiting time, and service rate.Source: §2.3 · pp. 11–12
3. System Optimization using Bayesian Optimization
The framework uses Bayesian optimization to tune MoD fleet size and pricing against an equilibrium performance objective. It combines a Gaussian Process surrogate, an acquisition rule, and a provider-focused objective while noting broader potential policy and planning applications.
3. System Optimization using Bayesian Optimization
- The optimization treats the inner-loop equilibrium simulation as a black-box objective and uses a surrogate posterior to choose the next supply-side parameters for evaluation.The performance measure can vary by stakeholder, such as operator profit or policy-maker consumer surplus and vehicle miles traveled.Source: §3 · pp. 12–13
- Because evaluations are expensive, noisy, and lack an analytic form, the authors use Bayesian optimization to search for optimal MoD fleet size and pricing parameters.The approach selects a candidate, evaluates the objective, updates the surrogate with the observation, and repeats.Source: §3 · pp. 12–13
3.1. Surrogate Model
- The Gaussian Process surrogate predicts the objective from historical observations and uses a Matérn covariance kernel with smoothness parameter ς = 5/2 in the experiments.The GP prediction provides a mean and variance at a candidate point.Source: §3.1 · p. 14
3.1.1. Acquisition Function
- The acquisition rule balances exploration and exploitation; the authors use GP-UCB, with κ updated automatically and δ = 0.1 in their experiments.The acquisition function uses surrogate predictions to select the next objective evaluation.Source: §3.1.1 · p. 15
3.2. Objective Function
- The provider-focused objective maximizes profit, defined as revenue minus operating costs, with fleet sizes and service-tier fare discounts as decision variables.Higher-capacity MoD fares apply a discount factor to the ride-hailing fare.Source: §3.2 · pp. 15–16
- Although the experiments define the objective from the service provider’s perspective, the framework is also presented as applicable to policy, subsidy, regulation, infrastructure, and transit-service planning.The paper identifies these as potential uses in multimodal systems with MoD.Source: §3.2 · p. 16
4. Numerical Experiments
The experiments test equilibrium convergence, transit-ASC calibration, Bayesian optimization (BO), discount-factor scenarios, and a ride-hailing tax using Manhattan taxi demand and four travel modes. They report a 15% profit advantage for BO over random search at real scale and quantify operational and stakeholder effects of the modeled scenarios.
4.1. Convergence to an Equilibrium
- Mode shares stabilized after about five iterations in test case 1; in test case 2, ride-hailing share fell and ridepooling share rose rapidly in the first five.The second case used a smaller ride-hailing fleet, while ridepooling had 1,000 vehicles; short trips and the unsatisfied-demand penalty help explain ride-hailing’s continued large share.Source: §4.1 · pp. 17–18, Figure 3 · p. 17, Figure 2 · p. 17
4.2. Calibrating the Alternative Specific Constant of Transit.
- Setting transit ASC to −3 yielded a 6.3% transit share; in test case 2, ride-hailing and ridepooling shares became 5.8% and 52.6%, respectively.Without ASCs, those shares were 20.8% and 19.9%.Source: §4.2 · p. 19, Table 4 · p. 19, Figure 4 · p. 19
4.3. Algorithm Performance.
- Full enumeration of 2,912 parameter settings yielded a best profit of 13,001; BO’s best profit was 12,674, about 2.5% lower, with EI and UCB performing similarly and PI worse.Source: §4.3 · p. 20
- BO’s solution increased profit by 15% over random search, with highest profits of 145,015 and 126,308, respectively.Source: §4.3 · p. 21
4.4. Scenario Analysis.
- Discount-factor functions produced positive discounts for all MoD services; in scenario 3, the micro-transit fleet was 19 as high low-discount disutility constrained its profitability.The BO search explored a broad decision-variable domain while concentrating more on regions with high expected profits.Source: §4.4 · pp. 22–24, Table 6 · p. 22, Figure 9 · p. 23
- With discount-factor functions, around 60% of demand went to ride-hailing, versus around 70% to high-capacity MoD in the base case, and profit was lower.Higher operating costs and discounts contributed to the lower profit; Table 7 reports the mode shares.Source: §4.4 · pp. 22–23, Table 7 · p. 23
- Across discount multipliers, profit first increased and then quickly decreased; the highest profit occurred at the BO-selected discount factors.As discounts increased, transit share fell while ridepooling and micro-transit shares rose; micro-transit share increased faster.Source: §4.4 · p. 24, Figure 10 · p. 24, Figure 11 · p. 24
4.5. An Application: Per-ride Tax
- A $2 per-ride tax absorbed by the provider decreased MoD vehicle miles traveled by 10.5% and profit by 30.5%.Public transit agency revenue increased by $14,340, while transit share rose by 1.6%.Source: §4.5 · p. 25, Table 8 · p. 25
5. Conclusion
The framework integrates mode choice into MoD system design and optimizes supply-side parameters, while allowing demand to respond to service levels. Numerical experiments demonstrate convergence, BO performance, and the framework’s use in quantifying policy effects across stakeholders.
5. Conclusion
- The framework integrates endogenous mode choice with MoD operations and uses Bayesian optimization to optimize supply-side parameters such as fleet size and fare.It allows MoD services to interact with competing travel modes.Source: §5 · p. 25
- Numerical experiments establish convergence and show BO outperforming random search in the Manhattan case study, calibrated with NYC stated-preference data.The case study includes ride-hailing, ridepooling, micro-transit, and public transit.Source: §5 · p. 26
- The framework quantifies a ride-hailing tax scenario in which transit ridership rises, MoD vehicle miles traveled and operator profit fall, and high-capacity services need larger discounts.The analysis considers consequences for government, passengers, and MoD operators.Source: §5 · p. 26
- Future work includes analytical equilibrium guarantees, more robust perception-sensitive choice models, and richer transit routing, whose assignment adds supply-demand dependencies.The study uses MNL because its closed-form choice probabilities integrate simply with the MoD simulation; the authors note sensitivity to choice-model parameters.Source: §5 · pp. 26–27