Michał Bujak

List of main publications and preprints

1. EJOR

   Balancing profit and traveller acceptance in ride-pooling personalised fares

   Bujak, Michał, and Kucharski, Rafał

   European Journal of Operational Research 2025

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   In a ride-pooling system, travellers experience discomfort associated with a detour and a longer travel time, which is compensated with a sharing discount. Most studies assume homogeneous travellers that receive either a flat discount or, in rare cases, a proportional to the inconvenience. This simplified approach offers inaccurate results and leads to an underperforming service when tested against diverse and natural human behaviour. We improve the standard approach on two bases. First, we propose a stochastic setting, where we leverage the population distribution of behavioural traits to determine the acceptance probability. Second, we personalise fares. Each traveller receives a sharing discount based on their contribution to the system such that the operator maximises his expected profitability. In the study, we rigorously prove that the discount optimisation problem can be decomposed. We optimise discounts at a ride level to claim the system optimum. An operator, when proposing fares, encounters two counteracting effects. Low fares increase realisation probability while high fares improve profit from a realised ride. In the personalised discount optimisation, we seek the golden mean. Travellers, who are well-aligned and experience minimal discomfort of sharing, are offered higher fares than those who require more incentive to join the service. Unlike in previous methods, our approach naturally balances the travellers satisfaction and the profit maximisation. With an experiment set in NYC, we show that this leads to significant improvements over the flat discount baseline: the mileage is reduced by 4.5% and the operator generates more profit per mile (over 20% improvement)

2. SNAM

   Optimising network efficiency in an epidemic scenario

   Proszewska, Magdalena, Bujak, Michal, Kucharski, Rafal, Tabor, Jacek, and Smieja, Marek

   Social Network Analysis and Mining 2025

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   Efficiency of a system network often relies on high connectivity. However, strongly connected networks are vulnerable in a case of a spreading virus. In our study, we propose a clustering method which balances the two opposing factors: maintains a high system efficiency yet minimises the spreading potential. Our Deep Epidemic Efficiency Network (DEEN) model leverages Graph Convolutional Neural Networks and a novel loss function. In an unsupervised setting, we seek a partition that maximises the system utility while restraining the transmission rate to a desired level. We show that proposed method successfully solves three real-life problems: ride-pooling service in New York City, economic exchange between regions in Poland, and information sharing via peer-to-peer network. In particular, by dividing 150 New York taxi travellers into four groups our method increases epidemic threshold more than twofold at the cost of reducing utility only by 13%. The model can be instrumental in future pandemic outbreaks when we need to balance between efficiency and potential spread of a virus.

3. J. public transp.

   SimFLEX: A methodology for comparative analysis of urban areas for implementing new on-demand feeder bus services

   Vasiutina, Hanna, Shulika, Olha, Bujak, Michał, Ghasemi, Farnoud, and Kucharski, Rafał

   Journal of Public Transportation 2025

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   On-demand feeder bus services present an innovative solution to urban mobility challenges, yet their success depends on a thorough assessment and strategic planning. Despite their potential, a systematic methodology for selecting suitable service areas remains underdeveloped. Simulation Framework for Feeder Location Evaluation (SimFLEX) utilizes spatial, demographic, and transportation-specific characteristics to conduct simulations at a microscopic level and compute various key performance indicators (KPIs), including service attractiveness, waiting time reduction, and added value. To address the stochastic nature of demand and uncertainty embedded in mode choice, we leverage Monte Carlo analysis, capturing variability across simulated scenarios. Our framework integrates several methods for a complete assessment of feeder potential: microscopic demand generation, creation of shared rides, public transport modeling, and iterative traveler learning and stabilization approach. Once the system stabilizes, KPIs are computed for comparative and sensitivity analyzes. As a showcase for our method, we apply SimFLEX to compare two remote districts in Krakow, Poland – Bronowice and Skotniki – designated as candidates for service deployment. Despite similar urban characteristics, our analysis revealed notable differences in KPIs between the analyzed areas: Skotniki exhibited higher service attractiveness (around 30 %) and added value (up to 7 %), whereas Bronowice showed greater potential for reducing waiting times (around 77 %). To assess the robustness of SimFLEX outputs under uncertain behavioral assumptions, we conducted a sensitivity analysis across a range of alternative-specific constants. The results consistently confirmed Skotniki as the more suitable candidate for feeder service implementation, demonstrating that this conclusion holds despite variations in a key preference parameter. The SimFLEX framework can be instrumental for decision makers to estimate feeder potential for a designated area. The model’s flexibility and modular characteristics make it a versatile tool for policymakers and urban planners to enhance urban mobility.

4. arXiv

   Wardropian Cycles make traffic assignment both optimal and fair by eliminating price-of-anarchy with Cyclical User Equilibrium for compliant connected autonomous vehicles

   Hoffmann, Michał, Bujak, Michał, Jamróz, Grzegorz, and Kucharski, Rafał

   arXiv preprint arXiv:2507.19675 2025

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   Connected and Autonomous Vehicles (CAVs) open the possibility for centralised routing with full compliance, making System Optimal traffic assignment attainable. However, as System Optimum makes some drivers better off than others, voluntary acceptance seems dubious. To overcome this issue, we propose a new concept of Wardropian cycles, which, in contrast to previous utopian visions, makes the assignment fair on top of being optimal, which amounts to satisfaction of both Wardrop’s principles. Such cycles, represented as sequences of permutations to the daily assignment matrices, always exist and equalise, after a limited number of days, average travel times among travellers (like in User Equilibrium) while preserving everyday optimality of path flows (like in System Optimum). We propose exact methods to compute such cycles and reduce their length and within-cycle inconvenience to the users. As identification of optimal cycles turns out to be NP-hard in many aspects, we introduce a greedy heuristic efficiently approximating the optimal solution. Finally, we introduce and discuss a new paradigm of Cyclical User Equilibrium, which ensures stability of optimal Wardropian Cycles under unilateral deviations. We complement our theoretical study with large-scale simulations. In Barcelona, 670 vehicle-hours of Price-of-Anarchy are eliminated using cycles with a median length of 11 days-though 5% of cycles exceed 90 days. However, in Berlin, just five days of applying the greedy assignment rule significantly reduces initial inequity. In Barcelona, Anaheim, and Sioux Falls, less than 7% of the initial inequity remains after 10 days, demonstrating the effectiveness of this approach in improving traffic performance with more ubiquitous social acceptability.

5. Transportation

   Ride-pooling service assessment with heterogeneous travellers in non-deterministic setting

   Bujak, Michal, and Kucharski, Rafal

   Transportation 2024

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   Ride-pooling remains a promising emerging mode with a potential to contribute towards urban sustainability and emission reductions. Recent studies revealed complexity and diversity among travellers’ ride-pooling attitudes. So far, ride-poling analyses assumed homogeneity of ride-pooling travellers. This, as we demonstrate, leads to a false assessment of ride-pooling system performance. We experiment with an actual NYC demand from 2016 and classify travellers into four groups of various ride-pooling behaviours (value of time and penalty for sharing), as reported in the recent SP study from Netherlands. We replicate their behavioural characteristics, according to the population distribution, to obtain meaningful performance estimations. Results vary significantly from the homogeneous benchmark: mileage savings were lower, while the utility gains for travellers were greater. Observing performance of heterogeneous travellers, we find that those with a low value of time are most beneficial travellers in the pooling system, while those with an average penalty for sharing benefit the most. Notably, despite the highly variable travellers’ behaviour, the confidence intervals for the key performance indicators are reasonably narrow and system-wide performance remains predictable. Our results show that the incorrect assumption of homogeneous traits leads to a high dissatisfaction of 18.5% and a cancellation rate of 36%. Such findings shed a new light on the expected performance of large scale ride-pooling systems.

6. JoTG

   Spatiotemporal variability of ride-pooling potential – Half a year New York City experiment

   Shulika, Olha, Bujak, Michal, Ghasemi, Farnoud, and Kucharski, Rafal

   Journal of Transport Geography 2024

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   Ride-pooling systems, despite being an appealing urban mobility mode, still struggle to gain momentum. While we know the significance of critical mass in reaching system sustainability, less is known about the spatiotemporal patterns of system performance. Here, we use 1.5 million NYC taxi trips (sampled over a six-month period) and experiment to understand how well they could be served with pooled services. We use an offline utility-driven ride-pooling algorithm and observe the pooling potential with six performance indicators: mileage reductions, travellers’ utility gains, share of pooled rides, occupancy, detours, and potential fleet reduction. We report distributions and temporal profiles of about 35 thousand experiments covering weekdays, weekends, evenings, mornings, and nights. We report complex spatial patterns, with gains concentrated in the core of the network and costs concentrated on the peripheries. The greatest potential shifts from the North in the morning to the Central and South in the afternoon. Offering pooled rides at the fare 32% lower than private ride-hailing seems to be sufficient to attract pooling yet dynamically adjusting it to the demand level and spatial pattern may be efficient. The patterns observed in NYC were replicated on smaller datasets in Chicago and Washington, DC, the occupancy grows with the demand with similar trends.

7. SNAM

   Network structures of urban ride-pooling problems and their properties

   Bujak, Michal, and Kucharski, Rafal

   Social Network Analysis and Mining 2023

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   Travellers, when sharing their rides in a so-called ride-pooling system, form complex networks. Despite being the algorithmic backbone to the ride-pooling problems, the shareability graphs have not been explicitly analysed yet. Here, we formalise them, study their properties and analyse relations between topological properties and expected ride-pooling performance. We introduce and formalise two representations at the two crucial stages of pooling analysis. On the NYC dataset, we run two simulations with the link generation formulas. One is when we increase discount offered to the travellers for shared rides (our control variable) and observe the phase transition. In the second, we replicate the non-deterministic behaviour of travellers in ride-pooling. This way, we generate probabilistic, weighted networks. We observed a strong correlation between the topological properties of ride-pooling networks and the system performance. Introduced class of networks paves the road to applying the network science methods to a variety of ride-pooling problems, like virus spreading, optimal pricing or stability analysis.