Large deviations for the capacity in dynamic spatial relay networks

TL;DR

This paper establishes a large deviation principle for user connection failures in dynamic relay networks, accounting for users entering and leaving the system, thus providing a more realistic model of network capacity behavior.

Contribution

It extends previous models by incorporating user departures, using advanced point process techniques to handle non-monotonic dynamics in relay network capacity analysis.

Findings

Large deviation principle derived for dynamic relay networks.

Model accounts for user arrivals and departures.

Techniques extend previous work to non-monotonic settings.

Abstract

We derive a large deviation principle for the space-time evolution of users in a relay network that are unable to connect due to capacity constraints. The users are distributed according to a Poisson point process with increasing intensity in a bounded domain, whereas the relays are positioned deterministically with given limiting density. The preceding work on capacity for relay networks by the authors describes the highly simplified setting where users can only enter but not leave the system. In the present manuscript we study the more realistic situation where users leave the system after a random transmission time. For this we extend the point process techniques developed in the preceding work thereby showing that they are not limited to settings with strong monotonicity properties.