Poisson Hail on a Wireless Ground

[2501.10712] Poisson Hail on a Wireless Ground Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Information Theory arXiv:2501.10712 (cs) [Submitted on 18 Jan 2025 ( v1 ), last revised 14 Apr 2026 (this version, v2)] Title: Poisson Hail on a Wireless Ground Authors: François Baccelli , Ke Feng , Sergey Foss View a PDF of the paper titled Poisson Hail on a Wireless Ground, by Fran\c{c}ois Baccelli and 2 other authors View PDF HTML (experimental) 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. Comments: submitted to IEEE Journal Subjects: Information Theory (cs.IT) ; Networking and Internet Architecture (cs.NI) Cite as: arXiv:2501.10712 [cs.IT] (or arXiv:2501.10712v2 [cs.IT] for this version) https://doi.org/10.48550/arXiv.2501.10712 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ke Feng [ view email ] [v1] Sat, 18 Jan 2025 09:52:55 UTC (175 KB) [v2] Tue, 14 Apr 2026 08:03:42 UTC (309 KB) Full-text links: Access Paper: View a PDF of the paper titled Poisson Hail on a Wireless Ground, by Fran\c{c}ois Baccelli and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.IT < prev | next > new | recent | 2025-01 Change to browse by: cs cs.NI math math.IT References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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