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arxiv: 2605.11798 · v1 · submitted 2026-05-12 · 💻 cs.CE

Recognition: 1 theorem link

· Lean Theorem

Advancing Dynamic Ride-Pooling Simulation -- A Highly Scalable Dispatcher

Kim Kandler, Moritz Laupichler, Peter Sanders, Peter Vortisch, Robin Andre

Pith reviewed 2026-05-13 04:46 UTC · model grok-4.3

classification 💻 cs.CE
keywords ride-poolingdynamic ride-poolingscalable dispatchershortest-path algorithmstransport simulationmode choice modelurban mobility
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The pith

Mt-KaRRi processes millions of ride-pooling requests per hour with response times around 1 millisecond.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces Mt-KaRRi as a dispatcher for dynamic ride-pooling that uses efficient shortest-path algorithms to handle large volumes of requests quickly. It incorporates a simple mode choice model and tests it on realistic travel demand from three urban areas. The key finding is that this design maintains low response times even at scales with millions of travelers and tens of thousands of vehicles. This capability opens the door to conducting detailed ride-pooling simulations that were not feasible before.

Core claim

Mt-KaRRi is a novel dispatcher for dynamic ride-pooling that leverages state-of-the-art shortest-path algorithms to process millions of travelers per hour while achieving a response time per request of around 1ms, even in the largest instances, enabling ride-pooling studies at unprecedented scale with tens of thousands of vehicles.

What carries the argument

Mt-KaRRi, the dispatcher that combines state-of-the-art shortest-path algorithms with a simple mode choice model to dynamically assign and route pooled rides.

If this is right

  • Quality of rides and vehicle resource usage can be analyzed for very large fleets and traveler volumes.
  • Simulations of ride-pooling in entire cities become practical with realistic demand data.
  • Future studies can explore how ride-pooling performs under different conditions at scales matching real-world operations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Such a scalable tool could support planning for autonomous vehicle fleets in mobility-on-demand services.
  • Researchers might use it to test the impact of varying mode choice behaviors on overall system efficiency.
  • Integration with real-time data could further enhance its applicability to live operations.

Load-bearing premise

That the shortest-path based matching combined with a simple mode choice model produces outcomes for ride quality and vehicle utilization that match real-world behavior in the tested urban areas.

What would settle it

Comparing the simulated average passenger wait times, ride durations, and vehicle occupancies against data from an actual ride-pooling service operating in one of the studied cities.

Figures

Figures reproduced from arXiv: 2605.11798 by Kim Kandler, Moritz Laupichler, Peter Sanders, Peter Vortisch, Robin Andre.

Figure 1
Figure 1. Figure 1: Search spaces for a point-to-point shortest-path query from 𝑠 to 𝑡 in the road network of Stuttgart, Germany, using Dijkstra’s algorithm (Figure 1a), the bidirectional variant of Dijkstra’s algorithm (Figure 1b), and a CH query (Figure 1c). Blue edges mark the search space of the forward query rooted at 𝑠 and red edges mark the search space of the reverse query rooted at 𝑡. Lines in Figure 1c include short… view at source ↗
Figure 2
Figure 2. Figure 2: Solid arrows indicate control flow. Dashed arrows indicate data reads and writes. Dotted lines indicate information for decisions. The node ∗ signifies a loop to the next event. Shortest-Path Queries for Meeting Points. As described in Section 3.1, meeting points are locations close to the origin or destination location of a vehicle at which the rider may be picked up or dropped off, requiring them to walk… view at source ↗
Figure 3
Figure 3. Figure 3: Solid arrows indicate control flow. Dashed arrows indicate data reads and writes. Dotted lines indicate information for decisions. The node ∗ signifies a loop to the next event. 4.3 Parallelization of KaRRi To reach the scalability required for the experiments in this paper, it does not suffice to find the best insertion and update the route state for every request one-by-one sequentially. Therefore, we in… view at source ↗
Figure 4
Figure 4. Figure 4: Distribution of trips over a whole weekday in our demand sets Karlsruhe (Tuesday), Stuttgart (Tuesday), and Los Angeles (Wednesday). Shows fraction of total trips per 15-minute interval of the day. For Los Angeles, the plot shows the distribution for the 100% population scale. The smaller scales have very similar distributions [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Shows entire country of Germany (Figure 5a) and the areas immediately surrounding Stuttgart (Figure 5b) and Karlsruhe (Figure 5c). Urban areas are shaded dark, rural areas are shaded light. Red boxes in Figure 5a show position of Stuttgart (right box) and Karlsruhe (left box) within Germany. For Figures 5b and 5c, the inner red outline indicates the limits of the city proper and the outer red outline indic… view at source ↗
Figure 6
Figure 6. Figure 6: Change in quality for different 𝑡batch compared to the non-batched version of KaRRi on KA and LA-25% with 50000 and 125000 vehicles, respectively. Shows the change for RP modal share, occupancy, and number of co-riders, as well as ride-detour, wait time, and system effectiveness. For explanations of the metrics, see Section 5.3. Note the logarithmic x-axis. run Rocky Linux 9.4. Our experiments on running t… view at source ↗
Figure 7
Figure 7. Figure 7: Average speedup of Mt-KaRRi with 𝑇 = 96 threads over sequential KaRRi for batch lengths 𝑡batch ∈ {1,2,5,15,30}. The LA-𝑝% instances use 𝑝 · 5000 vehicles, and the KA and ST instances use 50000 vehicles. Effect of 𝑡batch on Running Time. We now evaluate how the value of 𝑡batch affects the running time of the batch-parallel dispatcher. For this, we show the speedup over sequential KaRRi for 𝑇 = 96 threads an… view at source ↗
Figure 8
Figure 8. Figure 8: Ridership statistics for the LA-𝑝% instances with 𝑝 ∈ {0.1,1,5,10,25,50,100} using different fleet sizes. The x-axis describes the share of the population willing to use ride-pooling on a logarithmic scale. The y-axis of each plot describes the number of riders in millions (left) and the RP modal share (right). Note the different y-axis scales. For explanations of the metrics, see Section 5.3. 0.00 0.50 1.… view at source ↗
Figure 9
Figure 9. Figure 9: Pooling metrics on the LA-𝑝% instances with 𝑝 ∈ {0.1,1,5,10,25,50,100} using different fleet sizes. The x-axis describes the share of the population willing to use ride-pooling on a logarithmic scale. The y-axis shows the number of co-riders (left) and occupancy (right). Note the different y-axis scales. For explanations of the metrics, see Section 5.3. Number of Riders. The plots in [PITH_FULL_IMAGE:figu… view at source ↗
Figure 10
Figure 10. Figure 10: Quality metrics on the LA-𝑝% instances with 𝑝 ∈ {0.1,1,5,10,25,50,100} using different fleet sizes. The x-axis describes the share of the population willing to use ride-pooling on a logarithmic scale. The y-axis of each plot shows the ride detour, wait time, and system effectiveness, respectively. Note the different y-axis scales. For an explanation of the metrics, see Section 5.3. vehicle fleet considere… view at source ↗
Figure 11
Figure 11. Figure 11: Quality on KA with fleets 𝐹 of |𝐹| ∈ {10,20,30,40,50,75,100,150,200,300,400,500} · 103 vehicles and cap(𝜈) ∈ {2,4,8} for every 𝜈 ∈ 𝐹 with and without meeting points (MPs). The x-axis describes the number of vehicles in thousands. The y-axis shows (left to right, top to bottom) RP modal share, ride detour, average wait time, occupancy, number of co-riders, and system effectiveness, respectively. For explan… view at source ↗
Figure 12
Figure 12. Figure 12: Shows distribution of vehicles over number of passengers and time for a full day variant of KA with 25000 vehicles of capacity 4 (top), 25000 vehicles of capacity 8 (middle), and 50000 vehicles of capacity 4 (bottom). The height of each color stripe at a given point on the x-axis represents the number of vehicles that are currently idle (idle) or driving with 𝑘 passengers (𝑘 pax). We conduct experiments o… view at source ↗
Figure 13
Figure 13. Figure 13: Fraction of travelers per mode of transportation (PT = public transit, RP = ride-pooling) for the KA instance without ride-pooling (left) and with ride-pooling (right, 50000 vehicles). Shows distribution across modes for all requests (all), and subsets of urban-to-urban (u-u), rural-to-rural (r-r), urban-to-rural (u-r), and rural-to-urban (r-u) requests according to the RegioStaR-2 classification of Germa… view at source ↗
Figure 14
Figure 14. Figure 14: Top: Cumulative distribution of wait times and ride detours of performed rides on KA with 50000 vehicles. Bottom: Cumulative distribution of wait time and ride detour added to the originally offered ride after the rider has accepted the ride. We omit the top 0.1% of values to improve readability. Each line shows the distribution for one category of requests. than KaRRi without transfers, we would like to … view at source ↗
Figure 15
Figure 15. Figure 15: Shows RP modal share, ride detour, wait time, occupancy, average number of co-riders, and system effectiveness for varying detour cost parameters 𝑤detour ∈ {0,1,2,3} on the KA and LA-10% instances with 25000 vehicles. For an explanation of the metrics, see Section 5.3. Note the different y-axis scales. trip time of any existing rider 𝑟 to exceed 𝑡 max trip (𝑟), the insertion is considered infeasible. Thus… view at source ↗
Figure 16
Figure 16. Figure 16: Shows RP modal share, ride detour, wait time, occupancy, average number of co-riders, and system effectiveness for varying trip time constraint parameters 𝛼 ∈ {1.1,1.2,1.3,1.4,1.5} and 𝛽 ∈ {0,5,10,15,20} (in minutes) on the KA and LA-10% instances with 25000 vehicles. For an explanation of the metrics, see Section 5.3. Note the different y-axis scales. B.4 Walking Cost Parameter The walking cost parameter… view at source ↗
Figure 17
Figure 17. Figure 17: Shows RP modal share, ride detour, wait time, occupancy, average number of co-riders, and system effectiveness for varying maximum wait time 𝑡 max wait ∈ {0,2.5,5,7.5,10,12.5} (in minutes) on the KA and LA-10% instances with 25000 vehicles. For an explanation of the metrics, see Section 5.3. Note the different y-axis scales. We show absolute running times in [PITH_FULL_IMAGE:figures/full_fig_p029_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Shows RP modal share, ride detour, wait time, occupancy, average number of co-riders, and system effectiveness for varying walking cost parameters 𝑤walk ∈ {0,1,2,3} on the KA instance with 25000 vehicles. To determine meeting points, we use the rider-specific walking speed and maximum walking distance given by the KA instance. For an explanation of the metrics, see Section 5.3. Note the different y-axis s… view at source ↗
Figure 19
Figure 19. Figure 19: Shows absolute walking times (left) and normalized walking times (right) for varying walking cost parameters 𝑤walk ∈ {0,1,2,3} on the KA instance with 25000 vehicles. The normalized walking time on the right is defined as the median of the ratios between the walking time and the shortest-path travel time from origin to destination by car for every rider [PITH_FULL_IMAGE:figures/full_fig_p031_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Speedups of Mt-KaRRi over sequential KaRRi with different number of threads (logarithmic x-axis) on LA-1% with 5000 vehicles (left) and LA-25% with 50000 vehicles (right). Shows separate speedups for finding insertions, updating the system state, and the total running time. We do not show speedups for mode choice, since we did not parallelize it. Note the different y-axis scales. fraction of time 0.00 0.2… view at source ↗
Figure 21
Figure 21. Figure 21: Fraction of running time per component of non-batched KaRRi (no b.) and Mt-KaRRi with different numbers of threads 𝑇 on LA-1% (left) and LA-25% (right) with 5000 and 50000 vehicles, respectively. 32/35 [PITH_FULL_IMAGE:figures/full_fig_p032_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Quality on ST with fleets 𝐹 of |𝐹| ∈ {10,20,30,40,50,75,100,150,200,300,400,500} · 103 vehicles and cap(𝜈) ∈ {2,4,8} for every 𝜈 ∈ 𝐹 with and without meeting points (MPs). The x-axis describes the number of vehicles in thousands. The y-axis shows (left to right, top to bottom) RP modal share, ride detour, average wait time, occupancy, number of co-riders, and system effectiveness, respectively. For explan… view at source ↗
Figure 23
Figure 23. Figure 23: Fraction of travelers per mode of transportation (PT = public transit, RP = ride-pooling) for the ST instance without ride-pooling (left) and with ride-pooling (right, 50000 vehicles). Shows distribution across modes for all requests (all), and subsets of urban-to-urban (u-u), rural-to-rural (r-r), urban-to-rural (u-r), and rural-to-urban (r-u) requests according to the RegioStaR-2 classification of Germa… view at source ↗
read the original abstract

In ride-pooling, a fleet of vehicles is dynamically dispatched to bring travelers from A to B, trying to pool riders with similar itineraries to improve the use of resources compared to taxis or private cars. Ride-pooling is considered a core building block of future transport systems with autonomous vehicles. In this paper, we introduce Mt-KaRRi, a novel dispatcher for dynamic ride-pooling that leverages state-of-the-art shortest-path algorithms to process millions of travelers per hour. We add a simple mode choice model and use realistic travel demand in three different urban areas for extensive experiments. We find that our dispatcher scales well with a response time per request of around 1ms even for our largest instances. We show how this scalability can be used to conduct ride-pooling studies at unprecedented scale. For instance, we determine how the quality of rides and usage of vehicle resources develop for tens of thousands of vehicles and millions of travelers. We envision Mt-KaRRi as a tool for future ride-pooling simulation studies at scale.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper introduces Mt-KaRRi, a novel dispatcher for dynamic ride-pooling that leverages state-of-the-art shortest-path algorithms to process millions of travelers per hour. It incorporates a simple mode choice model and evaluates the approach on realistic travel demand data from three urban areas, reporting response times of around 1 ms per request even on the largest instances with tens of thousands of vehicles. The work demonstrates how this scalability enables ride-pooling studies at unprecedented scale, including analyses of ride quality and vehicle resource utilization for millions of travelers.

Significance. If the reported timings and scalability hold under end-to-end online conditions, the contribution is significant for the field of transportation simulation. It supplies a practical, high-performance tool that makes previously intractable large-scale ride-pooling experiments feasible, directly supporting research on autonomous-vehicle-based mobility systems. The use of multiple real-world demand datasets and the focus on online dynamic dispatching are positive aspects that increase the potential impact.

minor comments (3)
  1. [Results / Experiments] The abstract and results sections state the ~1 ms response time without accompanying variance, standard deviation, or per-component timing breakdown (shortest-path queries versus matching and assignment); adding these would strengthen verification of the end-to-end claim.
  2. [Methods] The simple mode choice model is introduced without explicit pseudocode or parameter values; a short algorithmic description or table of parameters would improve reproducibility.
  3. [Figures] Figure captions and legends for the large-scale utilization and ride-quality plots should explicitly state the demand dataset and fleet size corresponding to each curve to avoid ambiguity when comparing across the three urban areas.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, recognition of significance, and recommendation for minor revision. We are pleased that the scalability of Mt-KaRRi and its potential to enable large-scale ride-pooling studies are viewed favorably.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper introduces an algorithmic dispatcher (Mt-KaRRi) for dynamic ride-pooling and evaluates its scalability through direct empirical timing measurements on external urban travel demand datasets. The core claims rest on measured per-request response times (~1 ms) and instance sizes using standard shortest-path primitives plus a simple mode-choice model, rather than any derivation that reduces to fitted parameters, self-defined outputs, or load-bearing self-citations. No equations, uniqueness theorems, or ansatzes are presented that would create a self-referential loop; the performance results are falsifiable against the chosen datasets and algorithms.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, axioms, or invented entities are described. The work relies on standard shortest-path algorithms and realistic travel demand data whose details are not provided here.

pith-pipeline@v0.9.0 · 5488 in / 1129 out tokens · 30462 ms · 2026-05-13T04:46:18.981454+00:00 · methodology

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