Carl Dettmann

How far to the nearest facility?

For planning the road network, and provision of services, it is valuable to
know the distance from a typical point to the nearest facility. Examples
include electric vehicles requiring a charging station or pedestrians
requiring a taxi. Modelling the network and facilities as a Manhattan
Poisson line Cox process, and using path distance (that is, along roads)
we can find the distribution of the nearest facility from a typical point,
and the distribution of the "k"th nearest facility from a typical intersection.
Numerical simulations confirm the expressions obtained, as well as the
improvement in accuracy compared with simpler models.