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Geodesics and flows in a Poissonian city
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Kendall, W. S. (2009) Geodesics and flows in a Poissonian city. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2009 (No.43).
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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
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: | Working or Discussion Paper (Working Paper) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Library of Congress Subject Headings (LCSH): | Geodesics (Mathematics), Poisson processes | ||||
Series Name: | Working papers | ||||
Publisher: | University of Warwick. Centre for Research in Statistical Methodology | ||||
Place of Publication: | Coventry | ||||
Official Date: | 2009 | ||||
Dates: |
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Volume: | Vol.2009 | ||||
Number: | No.43 | ||||
Number of Pages: | 35 | ||||
Institution: | University of Warwick | ||||
Status: | Not Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 1 August 2016 | ||||
Date of first compliant Open Access: | 1 August 2016 |
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