  Aldous has introduced a notion of scale-invariant random spatial network
(SIRSN) as a mathematical formalization of road networks. Intuitively, those
are random processes that assign a route between each pair of points in
Euclidean space, while being invariant under rotation, translation, and change
of scale, and such that the routes are not too long and mainly on "main roads".
The only known example was somewhat artificial since invariance had to be added
at the end of the construction. We prove that the network of geodesics in the
random metric space generated by a Poisson line process marked by speeds
according to a power law is a SIRSN, in any dimension. Along the way, we
establish bounds comparing Euclidean balls and balls for the random metric
space. We also prove that in dimension more than two, the geodesics have "many
directions" near each point where they are not straight.
