# Spatial random multiple access with multiple departure

## TL;DR

This paper introduces a spatial random multiple access model with a unique departure policy where transmitting a message removes it and its neighbors within a radius, analyzing stability across different protocols.

## Contribution

It presents a novel spatial model with a non-standard departure policy and analyzes stability for various centralized and decentralized protocols.

## Key findings

- Stability conditions are derived for different protocols.
- The model exhibits unique asymptotic properties.
- Decentralized protocols with binary feedback are effective.

## Abstract

We introduce a new model of spatial random multiple access systems with a non-standard departure policy: all arriving messages are distributed uniformly on a finite sphere in the space, and when a successful transmission of a single message occurs, the transmitted message leaves the system together with all its neighbours within a ball of a given radius centred at the message's location. We consider three classes of protocols: centralised protocols and decentralised protocols with either ternary or binary feedback; and analyse their stability. Further, we discuss some asymptotic properties of stable protocols.