Traffic flow densities in large transport networks
- Hirsch, Christian
- Jahnel, Benedikt
- Keeler, Paul
- Patterson, Robert I. A.
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.
- Adv. Appl. Probab., 49 (2017), pp. 1091--1115, DOI 10.1017/apr.2017.35 .