Traffic flow densities in large transport networks. (17th November 2017)

• Record Type: Journal Article
• Authors: Hirsch, Christian; Jahnel, Benedikt; Keeler, Paul; Patterson, Robert I. A.
• Is Part Of: Advances in applied probability. Volume 49:Number 4(2017)
• Page Start: 1091
• Page End: 1115
• Publication Date: 2017-11-17
• Subjects: Traffic density, -- routeing, -- navigation, -- transport network, -- sub-ballisticity; Primary 60K30, -- 60F15, -- 90B20; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2017.35
• Languages: English
• ISSNs: 0001-8678

Abstract

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.