Poisson Hail on a Wireless Ground

2025-01-18

AI Summary

This paper investigates system stability in wireless networks under the coupled effects of spatial interference, dynamic user arrivals, and carrier-sense multiple access (CSMA). We propose the first Markovian modeling framework integrating spatial queuing, sensing delay, and distributed medium access. Leveraging stochastic geometry and Markov processes on counting measures, we rigorously characterize the non-monotonic impact of carrier sensing on stability: moderate backoff—i.e., non-greedy access—can restore stability to an otherwise unstable system, revealing a novel “restraint enables sustainability” stability principle. We derive an exact critical arrival rate for stability and prove that, under typical parameters, carrier sensing transforms previously unstable regimes into stable ones. This provides the first rigorous theoretical foundation for CSMA-based protocols such as Wi-Fi, bridging a long-standing gap between empirical deployment and analytical stability guarantees.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Stochastic Optimization
• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Wireless Networks
• Stability Analysis
• Resource Allocation

Innovation

• Wireless Communication Model
• Stability Analysis
• Cooperative Resource Sharing