I am a graduate of the applied mathematics at the Jagiellonian University. During my studies, I focused mostly on the probability theory (master’s thesis on the construction of the Wiener process), statistics and graph theory (bachelor’s thesis on the equivalence of Konig’s and Hall’s theorems). Currently, I am pursuing a PhD in the technical computer science at the same university.
My main field of expertise is the application of network science in the ride-pooling problem. My first contribution is the formalisation of network structures present in the algorithmic approach and the introduction of weighted structures. Later, I applied probabilistic tools to analyse the impact of behavioural heterogeneity of travellers on the system performance. Currently, I am working on the application of graph neural networks in the ride-pooling.
List of main publications and preprints
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Network structures of urban ride-pooling problems and their properties
Bujak, Michal,
and Kucharski, Rafal
Social Network Analysis and Mining
2023
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.
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Exploring shareability networks of probabilistic ride-pooling problems
Bujak, Michal,
and Kucharski, Rafał
arXiv preprint arXiv:2206.12259
2022
Travellers sharing rides in ride-pooling systems form various kinds of networks. While the notions of the so-called shareability graphs, has been in the core of many ride-pooling algorithms, so far they have not been explicitly analysed. Here, we introduce and examine four kinds of networks resulting from ride-pooling problems. We use 147 NYC taxi requests from 2016 pooled into attractive shared-rides with our utility based ExMAS algorithm and explore resulting shareability networks. To cover unknown individual properties of pooling travellers, we run 1000 replications of probabilistic pooling process, resulting in richer representation of weighted graphs instrumental to reveal complex network structures. Our findings reveal substantial differences between network structures and topologies. Properties of ride-pooling networks may be further analysed to better understand and improve ride-pooling systems.
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Ride-pooling service assessment with rational, heterogeneous, non-deterministic travellers
Bujak, Michal,
and Kucharski, Rafal
arXiv preprint arXiv:2307.10827
2023
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 aptitudes. So far, ride-poling analyses assumed homogeneity and/or determinism 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. We replicate their random behaviour to obtain meaningful distributions. Unsurprisingly, results vary significantly from the deterministic benchmark: expected 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. Such findings shed a new light on the expected performance of large scale ride-pooling systems. We argue, that the policy recommendations shall be revised to accommodate behavioural heterogeneity.
