Shortest Path Lengths in Poisson Line Cox Processes: Approximations and Applications

TL;DR

This paper derives exact and bounded expressions for shortest path lengths in Poisson line Cox processes, with applications in vehicle communication and urban charging infrastructure planning.

Contribution

It provides new analytical formulas and bounds for shortest path lengths in PLCPs, including conditions for tightness and comparisons between different path restrictions.

Findings

Exact expressions for shortest path lengths from typical points and intersections.

Bounds on shortest path lengths for two-turn cases and conditions for tightness.

Application frameworks for V2V communication and urban EV charging planning.

Abstract

We derive exact expressions for the shortest path length to a point of a Poisson line Cox process (PLCP) from the typical point of the PLCP and from the typical intersection of the underlying Poisson line process (PLP), restricted to a single turn. For the two turns case, we derive a bound on the shortest path length from the typical point and demonstrate conditions under which the bound is tight. We also highlight the line process and point process densities for which the shortest path from the typical intersection under the one turn restriction may be shorter than the shortest path from the typical point under the two turns restriction. Finally, we discuss two applications where our results can be employed for a statistical characterization of system performance: in a re-configurable intelligent surface (RIS) enabled vehicle-to-vehicle (V2V) communication system and in electric vehicle charging point deployment planning in urban streets.