Hyper pooling private trips into high occupancy transit like attractive shared rides

Ride-pooling is positioned between private ride-hailing and public transport but in practice remains closer to private rides in occupancy and efficiency. Existing pooled services are typically door-to-door and optimized for operations, often neglecting user attractiveness. The scalability limits of ride-pooling, especially for high-order pooling, remain unclear due to the combinatorial explosion of the matching search space. This study seeks to increase ride-pooling efficiency by boosting occupancies and reducing vehicle mileage while maintaining user attractiveness. The authors introduce hyper-pooled rides, in which travellers walk to common pick-up points, ride together across a sequence of intermediate stops, and then walk from common drop-off points to their destinations. The approach is bottom-up and utility-driven, building from individual private requests to door-to-door pooled rides, then to compact stop-to-stop rides, and finally bundling those into hyper-pooled multi-stop rides. By leveraging explicit user-utility formulations and shareability graph properties (building on the ExMAS algorithm), the method restricts the search to mutually attractive combinations, enabling identification of high-degree pooling solutions that would otherwise be intractable.

Foundational works introduced shareability networks and dynamic trip-vehicle assignment that enable efficient real-time pooling (e.g., Santi et al., 2014; Alonso-Mora et al., 2017). Subsequent research improved computational heuristics, spatial decomposition, and demand prediction to scale pooling. Behavioural studies quantified willingness to share, detour penalties, and variability effects, integrating them into utility-based demand models. Introducing pick-up/drop-off points (PUDOs) has been shown to reduce mileage and raise occupancy, though solutions often focus on operator cost savings. The ride-pooling problem shares similarities with on-demand public transport and benefits from economies of scale akin to the Mohring effect, though public transport typically starts with fixed lines, whereas this study adopts a demand-first, hierarchical aggregation. Recent work integrates fixed and flexible services via agent-based models and shows efficiency gains of demand-responsive services in certain contexts. However, the potential from bundling beyond standard pooling, without predefined lines, and the scalability to high-degree pooling remain insufficiently explored. This paper positions hyper-pooling to bridge gaps between current ride-pooling and transit-like operations through user-centric, utility-based, offline planning.

The study proposes a hierarchical, utility-based, offline algorithm termed hyper-pool. Input consists of disaggregated trip requests (origins, destinations, desired departure times) over a road network. The method proceeds in stages: (1) use ExMAS to enumerate all attractive door-to-door pooled rides; (2) compress selected door-to-door rides into compact stop-to-stop rides by optimizing a common pick-up point, a common departure time, and a common drop-off point within a maximum walking-time radius; (3) treat each stop-to-stop ride as a trip-like entity and pool these again with a modified ExMAS to form hyper-pooled multi-stop rides; (4) solve a coverage assignment problem to select rides system-wide, minimizing vehicle-hours while ensuring rides are attractive for all included travellers. Utility formulations: Private ride utility depends on direct travel time (weighted by traveller-specific value of time) and distance-based fare. Door-to-door pooled ride utility adds delay and in-vehicle sharing discomfort penalties, compensated by a pooling discount. For stop-to-stop rides, travellers incur access/egress walking times (with higher disutility multipliers) and benefit from fewer stops and potentially shorter in-vehicle times; attractiveness is required versus door-to-door pooling for all co-travellers. The algorithm finds optimal stop locations and common departure times by enumerating candidate pick-up points within τmax walking threshold, computing the squared-sum-delay-minimizing departure time for each candidate, and then enumerating candidate drop-off points; a log-sum expression balances utilities across co-travellers to avoid imbalances. Hyper-pooling bundles mutually exclusive stop-to-stop rides (no overlapping travellers), applying an additional discount and lower sharing penalty, ensuring the resulting hyper-pooled ride remains attractive versus private for all included travellers. Pairwise shareability of stop-to-stop rides is used to construct a shareability graph explored to increasing degrees, akin to ExMAS. Assignment: After generating the feasible set of private, door-to-door, stop-to-stop, and hyper-pooled rides, a binary coverage problem assigns each trip to exactly one ride. The objective minimizes vehicle-hours (operator perspective) because the ride generation already guarantees user attractiveness. Key performance indicators are computed: vehicle-hours, passenger utilities and components (fare, in-vehicle time, walk), fare-efficiency (€/veh-hour), and time-averaged effective occupancy. Implementation uses OSM network for travel times (fixed speeds: walking 1.5 m/s, vehicle 8 m/s), GTFS plus OpenTripPlanner for PT attributes. Experiment settings included Amsterdam PM peak demand, private fare 1.5 €/km, pooling discounts: 25% (door-to-door), 66% (stop-to-stop), 75% (hyper), in-vehicle time multiplier 1.3 for pooling, walk 1.5, wait 1.2, and traveller value of time normally distributed around 12 €/h. The algorithm is open-source and runs offline; batches up to 2000 trips per 10 minutes are solved in under 2 hours on a laptop, with the main bottleneck at the hyper-pooling step due to many feasible rides.

• Case study scale: For 2000 Amsterdam trips requested within 30 minutes, the algorithm identified over 1,000,000 feasible hyper-pooled rides. The final system solution assigned 225 travellers to 40 hyper-pooled rides, averaging 5.6–5.8 travellers per ride (maximum 14).
• Vehicle-hours reduction: If the 225 travellers rode privately, they would require 52.5 vehicle-hours; hyper-pooled multi-stop rides reduce this sixfold to 9 vehicle-hours. At the full-system level, average per-traveller vehicle-hours drop from 0.137 (private-only solution) to 0.086 when all pooling services are available.
• Occupancy: Average occupancy among pooled services increases, reaching 1.60 with hyper-pooling (vs. 1.53 door-to-door). Hyper-pooled rides themselves achieve much higher per-ride occupancies, up to 14.
• User utility: Mean per-traveller generalised cost improves from −7.56 € (private) to −6.65 € (with hyper-pooling). Hyper-pooling yields notable utility gains over door-to-door and stop-to-stop pooling and is attractive to both low and high value-of-time travellers.
• Fare and provider efficiency: Average fare per traveller decreases from 5.92 € (private) to 4.02 € (all pooling). Revenue per vehicle-hour increases from 43 €/veh-hour (private) to 50.8 for door-to-door, and is 47 €/veh-hour with hyper-pooling—still above private rides but below door-to-door.
• Illustrative 10-traveller bundle: 10 requests totalling 65 km privately are served by a single 9.6 km hyper-pooled multi-stop ride, reducing vehicle-hours from 2.25 to 0.44; total walking time 78 min; in-vehicle time 157 min; total disutility drops from 127 € to 95 €, and collected fare from 97 € to 24 €.
• Role of stop-to-stop: Stop-to-stop rides alone are often short and not substantially more attractive than door-to-door; they are instrumental intermediate constructs enabling hyper-pooled rides with substantial gains.
• Sensitivity: Raising hyper-pool price from 0.375 to 0.5 €/km causes about 30% of previously satisfied individuals to opt out, and 70% of hyper-pooled rides to have at least one unsatisfied member (disintegrating). With value of time at 12 €/h, hyper-pooling is attractive versus PT for ~80% of travellers; nearly 100% at 8 €/h; at 16 €/h, only ~40% versus private and ~20% versus PT.

The findings show that a bottom-up, utility-driven hierarchical approach can overcome practical limits to high-order pooling by selectively searching mutually attractive combinations. Hyper-pooling achieves transit-like occupancies and significant vehicle-hour reductions while maintaining traveller attractiveness, thereby addressing the dual goals of efficiency and user acceptance. Although stop-to-stop rides contribute limited direct utility improvement, they provide the structural building blocks for hyper-pooled rides that unlock substantial benefits. From a provider perspective, door-to-door pooling yields the highest revenue per vehicle-hour, but hyper-pooling remains more efficient than private rides, indicating that high-occupancy, discounted services can still be financially reasonable without subsidies under certain settings. Hyper-pooled rides appeal to a broad range of values of time, suggesting inclusivity beyond expected low-VOT users. The approach offers system-level benefits (lower mileage, higher occupancy) with modest walking, hinting at potential positive feedback loops (increased attractiveness, induced demand) and complementarity with public transport.

This paper introduces hyper-pooled rides and a hierarchical, utility-based algorithm that scales pooling beyond current limits by bundling compact stop-to-stop rides. The method identifies high-occupancy, multi-stop rides that are mutually attractive, significantly reducing vehicle-hours and user disutility while keeping fares low. Results from Amsterdam demonstrate up to 14-passenger rides, sixfold vehicle-hour reductions for the hyper-pooled subset, and system-wide improvements across key performance indicators. The open-source, reproducible framework can inform ride-pooling service design and potentially inspire new approaches to transit network design, where recurring patterns of hyper-pooled rides may guide line planning. Future research should address real-time implementation, integration of fleet operations (including deadheading and repositioning), vehicle heterogeneity and costs, personalised pricing and revenue management, and policy frameworks that may treat high-occupancy on-demand services as public services when they deliver transit-like efficiencies.

• The search is not exhaustive; it is a heuristic hierarchical approach that restricts to mutually attractive combinations and may miss feasible rides.
• The algorithm operates offline; transferring to real-time operations remains open.
• Fleet operations are treated as exogenous; sufficient vehicle availability is assumed, and repositioning/deadheading are not modeled.
• Vehicle type and capacity costs are not included; minibuses required for high occupancies may alter cost-effectiveness.
• Stops are optimized primarily to minimize walking for co-travellers; small changes in stop locations/timing could further reduce vehicle detours.
• Computational bottleneck can occur in the hyper-pooling ExMAS run due to the large number of feasible rides; some identified rides (about 5% of travellers) may require post-processing to ensure individual attractiveness.
• Achieving high-degree pooling requires a critical mass of demand; results may vary with lower demand densities and different urban contexts.