Kendall, Wilfrid S. (2009) Geodesics and flows in a Poissonian city. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers).

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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)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of 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
Date:	2009
Volume:	Vol.2009
Number:	No.43
Number of Pages:	35
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/35230

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