WIAS Preprint No. 2221, (2016)

Traffic flow densities in large transport networks


  • Hirsch, Christian
  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Keeler, Paul
    ORCID: 0000-0002-2063-1075
  • Patterson, Robert I. A.
    ORCID: 0000-0002-3583-2857

2010 Mathematics Subject Classification

  • 60K30 60F15 90B20


  • traffic density, routing, navigation, transport network, sub-ballisticity




We consider transport networks with nodes scattered at random in a large domain. At certain local rates, the nodes generate traffic flowing 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.

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