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DOI: 10.4230/LIPIcs.AofA.2026.27

Asymptotics of Parking Search in Hyperfractal Networks

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

Published in: LIPIcs, Volume 381, 37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026)

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.

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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)

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@InProceedings{deperle_et_al:LIPIcs.AofA.2026.27,
  author =	{Deperle, Geoffrey and Fricker, Christine and Jacquet, Philippe and Mans, Bernard and Rigonat, Alessia},
  title =	{{Asymptotics of Parking Search in Hyperfractal Networks}},
  booktitle =	{37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026)},
  pages =	{27:1--27:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-435-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{381},
  editor =	{Panagiotou, Konstantinos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2026.27},
  URN =		{urn:nbn:de:0030-drops-262982},
  doi =		{10.4230/LIPIcs.AofA.2026.27},
  annote =	{Keywords: Recursive weighted networks, Mellin transform, Asymptotic analysis, Scaling laws}
}

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Asymptotics of Parking Search in Hyperfractal Networks

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