Abstract
We consider transport networks with nodes scattered at random in a large domain. At certain local rates, the nodes generate traffic flows according to some navigation scheme in a given direction. In the thermodynamic limit of a growing domain, we present an asymptotic formula expressing the local traffic flow density at any given location in the domain in terms of three fundamental characteristics of the underlying network: the spatial intensity of the nodes together with their traffic generation rates, and of the links induced by the navigation. This formula holds for a general class of navigations satisfying a link-density and a sub-ballisticity condition. As a specific example, we verify these conditions for navigations arising from a directed spanning tree on a Poisson point process with inhomogeneous intensity function.
Item Type: | Journal article |
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Faculties: | Mathematics, Computer Science and Statistics > Mathematics |
Subjects: | 500 Science > 510 Mathematics |
ISSN: | 0001-8678 |
Language: | English |
Item ID: | 53447 |
Date Deposited: | 14. Jun 2018, 09:53 |
Last Modified: | 13. Aug 2024, 12:42 |