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Geodesics and flows in a Poissonian city
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Kendall, Wilfrid S.. (2011) Geodesics and flows in a Poissonian city. Annals of Applied Probability, Vol.21 (No.3). pp. 801-842. ISSN 1050-5164
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Official URL: http://dx.doi.org/10.1214/10-AAP724
Abstract
The stationary isotropic Poisson line network was used to derive upper bounds on mean excess network-geodesic length in Aldous and Kendall (2008). This new paper presents a study of the geometry and fluctuations of near-geodesics in such a network. The notion of a "Poissonian city" is introduced, in which connections between pairs of nodes are made using simple "no-overshoot" paths based on the Poisson line process. Asymptotics for geometric features and random variation in length are computed for such near-geodesic paths; it is shown that they traverse the network with an order of efficiency comparable to that of true network geodesics. Mean characteristics and limiting behaviour at the centre are computed for a natural network flow. Comparisons are drawn with similar network flows in a city based on a comparable rectilinear grid. A concluding section discusses several open problems.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Statistics |
| Library of Congress Subject Headings (LCSH): | Geodesics (Mathematics), Poisson processes |
| Series Name: | Working papers |
| Journal or Publication Title: | Annals of Applied Probability |
| Publisher: | Institute of Mathematical Statistics |
| Place of Publication: | Coventry |
| ISSN: | 1050-5164 |
| Date: | June 2011 |
| Volume: | Vol.21 |
| Number: | No.3 |
| Page Range: | pp. 801-842 |
| Identification Number: | 10.1214/10-AAP724 |
| Status: | Peer Reviewed |
| URI: | http://wrap.warwick.ac.uk/id/eprint/37636 |
Data sourced from Thomson Reuters' Web of Knowledge
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Geodesics and flows in a Poissonian city. (deposited 04 Jul 2011 14:31)
- Geodesics and flows in a Poissonian city. (deposited 20 Sep 2011 11:59) [Currently Displayed]
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