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Asymptotics of Parking Search in Hyperfractal Networks

Authors Geoffrey Deperle, Christine Fricker , Philippe Jacquet , Bernard Mans , Alessia Rigonat

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Subject Classification

ACM Subject Classification
  • Mathematics of computing
Keywords
  • Recursive weighted networks
  • Mellin transform
  • Asymptotic analysis
  • Scaling laws

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Abstract

We study the asymptotic behaviour of the distance to the first available parking slot in a recursive Manhattan street network endowed with a hyperfractal intensity structure, where slot-release events occur according to Poisson processes along the streets.
We establish, by analysing the associated self-similar harmonic sums via Mellin-transform asymptotics [Flajolet et al., 1995], a power-law decay of the expected distance as the total intensity grows, with exponent equal to the inverse of the hyperfractal dimension. In particular, the scaling exponent depends only on the large-scale geometry of the network.
We further prove that this exponent is robust under random multiplicative modulations of the street intensities: mild stochastic heterogeneity affects only the multiplicative constant. Similar scaling behaviour holds for the variance, the number of turns before parking, and for a jump-over variant of the search strategy.

Cite As Get BibTex

Geoffrey Deperle, Christine Fricker, Philippe Jacquet, Bernard Mans, and Alessia Rigonat. Asymptotics of Parking Search in Hyperfractal Networks. In 37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 381, pp. 27:1-27:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.AofA.2026.27

Author Details

Geoffrey Deperle
  • INRIA, Palaiseau, France
Christine Fricker
  • INRIA, Paris, France
Philippe Jacquet
  • INRIA, Palaiseau, France
Bernard Mans
  • Macquarie University, Australia
Alessia Rigonat
  • INRIA, Paris, France

Funding

This work is funded by the French National Research Agency as part of the Mob Sci-Dat Factory project (ANR- 23-PEMO-0004) under the France 2030 program

References

  1. Michael Batty and Paul Longley. Fractal Cities: A Geometry of Form and Function. Academic Press, 1994. Google Scholar
  2. Geoffrey Deperle and Philippe Jacquet. Generating random hyperfractal cities. arXiv preprint, arXiv:2512.01505, 2025. URL: https://doi.org/10.48550/arXiv.2512.01505.
  3. Philippe Flajolet, Xavier Gourdon, and Philippe Dumas. Mellin transforms and asymptotics: Harmonic sums. Theoretical Computer Science, 144(1-2):3-58, 1995. URL: https://doi.org/10.1016/0304-3975(95)00002-E.
  4. Christine Fricker and Nicolas Gast. Incentives and redistribution in homogeneous bike-sharing systems with stations of finite capacity. EURO Journal on Transportation and Logistics, 5(3):261-291, 2016. URL: https://doi.org/10.1007/S13676-014-0053-5.
  5. Christine Fricker, Hanene Mohamed, and Alessia Rigonat. Stochastic averaging and mean-field for a large system with fast varying environment with applications to free-floating car-sharing. Queueing Systems, 109(4):1-27, 2025. Google Scholar
  6. Philippe Jacquet and Dalia Popescu. Self-similar geometry for ad-hoc wireless networks: Hyperfractals. In Geometric Science of Information, Lecture Notes in Computer Science, pages 522-529. Springer, 2017. Google Scholar
  7. Aaron Kolleck. Does car-sharing reduce car ownership? Empirical evidence from germany. Sustainability, 13(13):7384, 2021. Google Scholar
  8. Sarah Toy, Lorraine Whitmarsh, and Yixian Sun. Zero-car households - Constraint or lifestyle choice? A systematic literature review of the factors affecting non-car ownership. Transport Reviews, 45(3):390-412, 2025. Google Scholar
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