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Geodesics and flows in a Poissonian city
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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 networkgeodesic length in Aldous and Kendall (2008). This new paper presents a study of the geometry and fluctuations of neargeodesics in such a network. The notion of a "Poissonian city" is introduced, in which connections between pairs of nodes are made using simple "noovershoot" paths based on the Poisson line process. Asymptotics for geometric features and random variation in length are computed for such neargeodesic 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Status:  Not Peer Reviewed 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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