On the k Nearest-Neighbor Path Distance from the Typical Intersection in the Manhattan Poisson Line Cox Process
share
In this paper, we consider a Cox point process driven by the Manhattan Poisson line process. We calculate the exact cumulative distribution function (CDF) of the path distance (L1 norm) between a randomly selected intersection and the k-th nearest node of the Cox process. The CDF is expressed as a sum over the integer partition function p(k), which allows us to numerically evaluate the CDF in a simple manner for practical values of k. These distance distributions can be used to study the k-coverage of broadcast signals transmitted from a RSU located at an intersection in intelligent transport systems (ITS). Also, they can be insightful for network dimensioning in vehicle-to-everything (V2X) systems, because they can yield the exact distribution of network load within a cell, provided that the RSU is placed at an intersection. Finally, they can find useful applications in other branches of science like spatial databases, emergency response planning, and districting.
READ FULL TEXT