{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T14:58:14Z","timestamp":1777129094000,"version":"3.51.4"},"reference-count":10,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,5,21]],"date-time":"2024-05-21T00:00:00Z","timestamp":1716249600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"IPN SIP project","award":["20240671"],"award-info":[{"award-number":["20240671"]}]},{"name":"IPN SIP project","award":["20240675"],"award-info":[{"award-number":["20240675"]}]},{"name":"IPN SIP project","award":["20241113"],"award-info":[{"award-number":["20241113"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this study, we analyze the CSMA Non-Persistent protocol with a finite number of nodes, providing more accurate results for applications like wireless sensor networks. The finite model addresses scenarios where the node count is moderate, capturing realistic system dynamics. Our analysis reveals a dependency on the node count, impacting system throughput. As the node count increases, throughput behavior aligns with Kleinrock\u2019s infinite model. We derive a complex closed-form throughput expression for a finite quantity of nodes in the system, solved numerically, and offer an approximate expression for specific conditions. These insights advance understanding of low-contention network performance, especially in scenarios where the infinite model becomes inadequate.<\/jats:p>","DOI":"10.3390\/s24113290","type":"journal-article","created":{"date-parts":[[2024,5,22]],"date-time":"2024-05-22T07:56:11Z","timestamp":1716364571000},"page":"3290","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Performance Analysis of CSMA\/NP under Finite Population Environments"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-1301-2834","authenticated-orcid":false,"given":"Ariadna I.","family":"Rodriguez-Gomez","sequence":"first","affiliation":[{"name":"Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, Mexico City 07738, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1020-6806","authenticated-orcid":false,"given":"Mario E.","family":"Rivero-Angeles","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, Mexico City 07738, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2768-6009","authenticated-orcid":false,"given":"Izlian Y.","family":"Orea-Flores","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, Mexico City 07738, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5212-350X","authenticated-orcid":false,"given":"Gina","family":"Gallegos-Garc\u00eda","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, Mexico City 07738, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7134-0190","authenticated-orcid":false,"given":"Juan Carlos","family":"Chimal-Eguia","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, Mexico City 07738, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,21]]},"reference":[{"key":"ref_1","unstructured":"Ukhurebor, K.E., Odesanya, I., Tyokighir, S.S., Kerry, R.G., Olayinka, A.S., and Bobadoye, A.O. (2021). Wireless Sensor Networks: Applications and Challenges, IntechOpen eBooks."},{"key":"ref_2","first-page":"92","article-title":"Wireless Sensor Networks","volume":"41","author":"Stankovic","year":"2008","journal-title":"Sensors"},{"key":"ref_3","unstructured":"Abdirahman, M.J. (2024, January 17). Communication Protocols for Wireless Sensor Networks. Available online: https:\/\/www.researchgate.net\/publication\/358594142."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Huang, W., Lin, J., Chen, C.H., Chang, Y.-S., and Chen, Y.Y. (2010). Accurate Analysis of IEEE 802.15.4 Slotted CSMA\/CA over a Real-Time Wireless Sensor Network, Springer eBooks.","DOI":"10.1007\/978-3-642-11528-8_8"},{"key":"ref_5","first-page":"1247","article-title":"Finite Population CSMA\/CD Networks","volume":"31","author":"Coyle","year":"1983","journal-title":"IEEE Commun. Lett."},{"key":"ref_6","unstructured":"Wu, J.-L.C., Wu, J., and Lee, T.-C. (1988, January 27\u201331). 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Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2206","DOI":"10.1109\/TCOMM.2011.051811.100241","article-title":"Analysis of Non-Persistent CSMA Protocols with Exponential Backoff Scheduling","volume":"59","author":"Wong","year":"2011","journal-title":"IEEE Trans. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1400","DOI":"10.1109\/TCOM.1975.1092768","article-title":"Packet Switching in Radio Channels: Part I-Carrier Sense Multiple-Access Modes and their Throughput-Delay Characteristics","volume":"23","author":"Kleinrock","year":"1975","journal-title":"IEEE Trans. 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