A framework to integrate mode choice in the design of mobility-on-demand systems

The paper addresses how to design and operate Mobility-on-Demand (MoD) systems when demand is endogenous and interacts with other modes such as public transit. Prior work often assumes fixed demand for MoD and cannot assess broader system impacts like induced demand or transit ridership changes. The authors aim to integrate a behavioral mode choice model with a high-capacity MoD simulation to capture supply–demand feedbacks, and to optimize supply-side parameters (fleet sizes and fares/discounts) using Bayesian Optimization. The study’s purpose is to provide a practical, scalable framework for planning and policy analysis in multimodal settings where travelers choose among ride-hailing, pooled MoD, micro-transit, and public transit based on level-of-service attributes.

The study situates itself within research on MoD system design and operations, including dispatching and ride-pooling methods (e.g., shareability networks and dynamic trip-vehicle assignment enabling high-capacity pooling). Work on autonomous MoD (AMoD) has explored operations and impacts on environment, congestion, and parking. Studies integrating MoD with transit often focus on first/last-mile solutions and operational viability. Only a few efforts have modeled endogenous demand in multimodal contexts within agent-based platforms (e.g., MATSim, SimMobility), often using synthetic choice models and scenario analyses rather than supply optimization. Recent work on multimodal equilibrium and operator policy adjustments exists but emphasizes sensitivity analysis rather than optimal design. Competition among providers has been studied separately; the present work considers a single provider while noting integration of competitive models as future research.

The authors propose a two-level simulation-optimization framework. Inner loop (mode choice and operations): Travelers choose among four modes—ride-hailing (capacity 1), ridepooling (capacity 4), micro-transit (capacity 10), and public transit—based on a mode choice model. The choice model is an MNL estimated from a stated-preference survey of New York City residents (n=1507 after validation). The discrete choice experiment varied walking/waiting time, in-vehicle time, costs, powertrain, and automation for Uber-like and UberPool-like alternatives versus current mode. The MNL yields marginal utilities and willingness-to-pay values; alternative-specific constants (ASCs) are recalibrated for the case study demand. Mode-specific service attributes are updated iteratively based on simulated operations until mode shares converge (average change across modes < 1%). MoD operations are simulated following an anytime optimal dynamic trip-vehicle assignment framework: (1) construct request-vehicle and request-trip-vehicle graphs from shareability principles under constraints on max waiting time, max in-vehicle delay, and vehicle capacity; (2) solve an ILP to assign vehicles to feasible trips, using an objective combining total delay and penalties for unassigned requests (with an equivalent formulation reducing variables by omitting explicit unserved indicators); (3) rebalance idle vehicles via a linear program to likely demand locations. Assignments run every 60 seconds. Public transit service levels are computed by building a GTFS-based transit network, connecting it to the road network via walk links, and performing all-pairs shortest paths to obtain walk-transit-walk routes, expected waiting (half headway), and fares. Historical attributes by OD-cluster pairs are exponentially smoothed with parameter β=0.5. Service rates (served fractions) for MoD modes are tracked; utilities for next-iteration mode choices penalize unsatisfied MoD demand by blending with transit utility using a penalty multiplier c_m=2. Outer loop (Bayesian Optimization): The framework treats the inner-loop equilibrium objective as a black-box function of supply-side parameters x (fleet sizes and discount factors). A Gaussian Process surrogate with Matérn 5/2 kernel models the objective; an acquisition function (GP-UCB) selects the next x to evaluate, balancing exploration and exploitation with an automatically updated κ. Objective: Provider profit equals revenue minus costs. Base fares follow an UberX-like fare model; pooled modes apply discounts via factors γ_m, with fares f_r = (1 − γ)·max(f_min, f_base + f_t·t_r + f_d·d_r). Costs include driver salary ($17/hour), leasing (normalized daily costs: $11.97 sedan, $19.32 minivan scaled to the hour), and operating cost ($0.1473/mile). Data and setup: Manhattan taxi OD data (8–9 am, Monday May 6, 2013), road network (4092 nodes, 9453 edges), MTA subway GTFS. Initialization sets waiting and travel time heuristics by mode (e.g., maximum wait 10 min; scaling IVTTs 1.0x, 1.2x, 1.5x for capacities 1,4,10; initial waits 0.30, 0.362, 0.450 of max wait). Numerical experiments examine convergence, ASC calibration for transit, BO performance versus enumeration/random search, sensitivity to discount perception via scenario functions added to utility, and a per-ride tax policy.

- Mode choice model: Estimated MNL coefficients imply WTP to save an hour of time of $25.9 for out-of-vehicle time (OVTT) and $18.6 for in-vehicle time (IVTT). Sample size used in estimation: 1507 respondents. - Convergence: Inner loop mode shares stabilized within ~5 iterations in test cases; stopping criterion values fell below 0.01 (e.g., 0.0031 to 0.0018 in late iterations of test case 1; 0.0045 to 0.0018 in test case 2). - Transit ASC calibration: Setting transit ASC to −3 yielded an endogenously determined transit share of 6.3% for the study demand (targeting 0–10%). - BO vs exhaustive search (10% demand, fixed discounts): Grid enumeration of 2912 combinations found profit 13,001 at n1=225, n4=150, n10=0. BO found profit 12,674 at n1=182, n4=85, n10=99 (gap ≈ 2.5%). EI and UCB performed similarly; PI performed worse. - BO vs random search (full demand): With equal function evaluations, BO achieved a best profit of 145,015 versus 126,308 for random search (+15%). BO solution: n1=817, n4=1539, n10=173 with γ4=0, γ10=0 in the base case without additional discount-perception disutility. - Discount perception scenarios (adding f(γ) to utility): • Scenario 1 (low disutility): Optimal n1=2826, n4=235, n10=526; γ4=0.12, γ10=0.24; profit 122,838. Mode shares: ride-hailing 61.0%, ridepooling 13.5%, micro-transit 19.2%, transit 6.3%. • Scenario 2 (medium disutility): Optimal n1=2801, n4=428, n10=690; γ4=0.17, γ10=0.29; profit 119,154. Mode shares: ride-hailing 60.5%, ridepooling 14.8%, micro-transit 18.6%, transit 6.1%. • Scenario 3 (high disutility): Optimal n1=2900, n4=924, n10=19; γ4=0.33, γ10=0.69; profit 111,141. Mode shares: ride-hailing 62.2%, ridepooling 26.4%, micro-transit 6.4%, transit 5.0%. • In contrast, ignoring discount-perception disutility (base run) yielded ridepooling 56.1% and micro-transit 13.7% (≈70% high-capacity MoD), ride-hailing 23.2%, transit 7.0%. - Discount multipliers (holding fleet sizes at scenario optima): Profits typically peak near BO-chosen discounts; increasing discounts beyond optima initially increases shared-mode shares (especially micro-transit) but reduces profit due to revenue loss. - Policy analysis: Imposing a $2 per-ride tax on ride-hailing (provider absorbs cost) under Scenario 1 conditions: • Optimal under tax: n1=1388, n4=1668, n10=31; γ4=0.15, γ10=0.67; profit 100,748 vs 122,838 no-tax (−30.5%). • VMT falls from 33,835.7 to 30,288.3 (−10.5%); PMT/VMT ratio increases from 1.11 to 1.17. • Mode shares shift: ride-hailing 61.0%→36.4%, ridepooling 13.5%→50.6%, micro-transit 19.2%→5.1%, transit 6.3%→7.9% (transit +1.6 pp).

Integrating behavioral mode choice with MoD operations yields an endogenous demand framework that more realistically captures competition among ride-hailing, shared MoD, and transit. The inner-loop simulation converges reliably, demonstrating that the system reaches a consistent equilibrium in mode shares for given supply parameters. The BO-based outer loop efficiently navigates the expensive, noisy objective landscape and outperforms random search, achieving substantially higher provider profits with far fewer evaluations. Results underscore the critical role of user preferences and perceived discounts: when disutility for low discounts is incorporated, optimal policies require larger discounts and/or larger fleets for shared modes, reducing profits relative to the base case that ignores perception effects. The framework enables quantitative policy evaluation; for instance, a per-ride tax on ride-hailing reduces MoD VMT and shifts demand toward pooled services and transit while substantially lowering provider profits—highlighting trade-offs among congestion, mode shares, and operator viability. Overall, the findings validate the usefulness of the proposed framework in jointly assessing operational design and policy impacts in multimodal systems.

The paper introduces a unified framework that integrates a mode choice model with a state-of-the-art MoD simulator and uses Bayesian Optimization to select supply-side parameters such as fleet sizes and discounts. Calibrated on Manhattan taxi demand and a New York City SP study, the framework achieves convergence of the multimodal supply–demand system and demonstrates BO’s superiority over random search in optimizing operator profit. It also enables scenario and policy analyses, including the effects of discount perceptions and per-ride taxes on mode shares, VMT, and profitability. Future work includes: (i) formal analysis of equilibrium existence/uniqueness for the fixed-point inner loop; (ii) richer yet computationally tractable choice models capturing latent perceptions (e.g., reliability, sharing disutility, non-linear discount effects) while maintaining closed-form probabilities; (iii) more advanced transit assignment or hyperpath-based routing to capture demand-dependent transit performance; and (iv) extending to multi-operator competition and market equilibrium.

- Single MoD operator assumed; competition among providers and market equilibrium effects are not modeled. - Mode choice uses MNL for tractability; it may not capture heterogeneous preferences or complex perceptions (e.g., non-linear discount sensitivity, sharing aversion). ASCs from SP data required recalibration for the case study demand. - Transit representation is a route-planning model based on GTFS schedules, not a full transit assignment with crowding or demand-dependent travel times. - Optimization objective focuses on provider profit; alternative objectives (e.g., consumer surplus, system welfare) are not jointly optimized here. - Simulation outcomes are subject to stochastic noise (e.g., initial vehicle locations, probabilistic choices), and convergence guarantees are empirical rather than analytical. - Discount perception effects are introduced via ad hoc scenario functions rather than estimated within the choice model.