Poisson Hail on a Wireless Ground

TL;DR

This paper introduces a new wireless communication model combining interference, queue dynamics, and collision avoidance, showing that sensing can stabilize systems that would otherwise be unstable.

Contribution

It develops a Markov process framework for the model and characterizes the stability region, highlighting the stabilizing effect of collision avoidance.

Findings

Sensing and collision avoidance can stabilize otherwise unstable systems.

The model is represented as a Markov process on counting measures.

Critical arrival rates for stability are characterized.

Abstract

This paper defines a new model which incorporates three key ingredients of a large class of wireless communication systems: (1) spatial interactions through interference, (2) dynamics of the queueing type, with users joining and leaving, and (3) carrier sensing and collision avoidance as used in, e.g., WiFi. In systems using (3), rather than directly accessing the shared resources upon arrival, a customer is considerate and waits to access them until nearby users in service have left. This new model can be seen as a missing piece of a larger puzzle that contains such dynamics as spatial birth-and-death processes, the Poisson-Hail model, and wireless dynamics as key other pieces. It is shown that, under natural assumptions, this model can be represented as a Markov process on the space of counting measures. The main results are then two-fold. The first is on the shape of the stability region and, more precisely, on the characterization of the critical value of the arrival rate that separates stability from instability. The second is of a more qualitative or perhaps even ethical nature. There is evidence that for natural values of the system parameters, the implementation of sensing and collision avoidance stabilizes a system that would be unstable if immediate access to the shared resources would be granted. In other words, for these parameters, renouncing greedy access makes sharing sustainable, whereas indulging in greedy access kills the system.