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However, due to the unpredictable nature of end-user requests and the limited resource capacity of low Earth orbit (LEO) satellites, improper Virtual Network Function (VNF) deployment can lead to significant increases in end-to-end (E2E) delay. To address this challenge, we propose an online algorithm that jointly deploys VNFs and forms routing paths in an event-driven manner in response to end-user requests. The proposed algorithm selectively deploys only the essential VNFs required for each Service Function Chain (SFC), focusing on minimizing E2E delay\u2014a critical QoS parameter. By defining a minimum-hop region (MHR) based on the geographic coordinates of the routing endpoints, we reduce the search space for candidate base stations, thereby designing paths that minimize propagation delays. VNFs are then deployed along these paths to further reduce E2E delay. Simulations demonstrate that the proposed algorithm closely approximates the global optimum, achieving up to 97% similarity in both E2E delay and CPU power consumption, with an average similarity of approximately 90%.<\/jats:p>","DOI":"10.3390\/s24227286","type":"journal-article","created":{"date-parts":[[2024,11,14]],"date-time":"2024-11-14T10:47:53Z","timestamp":1731581273000},"page":"7286","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Online Service Function Chain Planning for Satellite\u2013Ground Integrated Networks to Minimize End-to-End (E2E) Delay"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0121-3588","authenticated-orcid":false,"given":"Soohyeong","family":"Kim","sequence":"first","affiliation":[{"name":"Major in Bio-Artificial Intelligence, Department of Computer Science and Engineering, Hanyang University, Ansan 15588, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0745-1475","authenticated-orcid":false,"given":"Joohan","family":"Park","sequence":"additional","affiliation":[{"name":"Spatial Wireless Networking Research Section, Electronics and Telecommunications Research Institute (ETRI), 218 Gajeong-ro, Yuseong-gu, Daejeon 34129, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6764-1855","authenticated-orcid":false,"given":"Jiseung","family":"Youn","sequence":"additional","affiliation":[{"name":"Major in Bio-Artificial Intelligence, Department of Computer Science and Engineering, Hanyang University, Ansan 15588, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8498-4577","authenticated-orcid":false,"given":"Seyoung","family":"Ahn","sequence":"additional","affiliation":[{"name":"Major in Bio-Artificial Intelligence, Department of Computer Science and Engineering, Hanyang University, Ansan 15588, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1847-6088","authenticated-orcid":false,"given":"Sunghyun","family":"Cho","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, Hanyang University, Ansan 15588, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"20442","DOI":"10.1109\/JIOT.2023.3286382","article-title":"Random Access Protocol for Massive Internet of Things Connectivity in Space\u2013Air\u2013Ground-Integrated Networks","volume":"10","author":"Park","year":"2023","journal-title":"IEEE Internet Things J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1109\/MCOM.2018.1700038","article-title":"The space-terrestrial integrated network: An overview","volume":"56","author":"Yao","year":"2018","journal-title":"IEEE Commun. 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