Geodesics and flows in a Poissonian city
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, Vol.2009 (No.43).
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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
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|
|Number of Pages:||35|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
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