{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T05:58:30Z","timestamp":1769752710786,"version":"3.49.0"},"reference-count":25,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T00:00:00Z","timestamp":1683244800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>LEO satellite mega-constellation projects have been proposed by many countries or commercial organizations in recent years. With more than 2000 satellites launched by SpaceX to configure the Starlink system, the orbital resources are more constrained given the existence of spacecrafts and countless orbital debris. Due to this, the operating environment is full of uncertainty and information symmetry is absent for designers and stakeholders during the process of project deployment. The flux model of space debris on orbit has been built for assessing the LEO operation environment. Based on the orbital debris flux model, the collision probability can be calculated, which is an important variable of the state space. Given the condition that tge number of satellites decreases due to collision between satellites and debris, the Markov decision model has been built for optimal deployment strategy and decision-making. In order to assure that the mega-constellation system could provide services when satellites have failed, additional satellites need to be launched. The optimal deployment is the decision to launch a moderate number of satellites to maximize the benefit and minimize the cost. Assuming that at least 30 satellites need to be operated, 4 deployment scenarios are considered and the optimal deployment strategies can be obtained.<\/jats:p>","DOI":"10.3390\/sym15051024","type":"journal-article","created":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T02:08:42Z","timestamp":1683252522000},"page":"1024","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Optimal Deployment Strategy of Mega-Constellation Based on Markov Decision Process"],"prefix":"10.3390","volume":"15","author":[{"given":"Xuefeng","family":"Wang","sequence":"first","affiliation":[{"name":"Research Center of Satellite Technology, School of Astronautics, Harbin Institute of Technology, Harbin 150000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shijie","family":"Zhang","sequence":"additional","affiliation":[{"name":"Research Center of Satellite Technology, School of Astronautics, Harbin Institute of Technology, Harbin 150000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongzhu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Research Center of Satellite Technology, School of Astronautics, Harbin Institute of Technology, Harbin 150000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1109\/MNET.011.2000493","article-title":"Non-terrestrial networks in the 6G era: Challenges and opportunities","volume":"35","author":"Giordani","year":"2021","journal-title":"IEEE Netw."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.actaastro.2019.03.040","article-title":"A technical comparison of three low earth orbit satellite constellation systems to provide global broadband","volume":"159","author":"Portillo","year":"2019","journal-title":"Acta Astronaut."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1108\/AEAT-07-2013-0131","article-title":"Close approach analysis of space objects and estimation of satellite-debris collision probability","volume":"87","author":"Navabi","year":"2015","journal-title":"Aircr. Eng. Aerosp. Technol. Int. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1016\/j.apm.2021.08.030","article-title":"Coupled Orbit-Attitude Dynamics and Trajectory Tracking Control for Spacecraft Electromagnetic Docking","volume":"101","author":"Shi","year":"2022","journal-title":"Appl. Math. Model."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2257","DOI":"10.1109\/TAES.2021.3130830","article-title":"Active Disturbance Rejection Control for Delayed Electromagnetic Docking of Spacecraft in Elliptical Orbits","volume":"58","author":"Liu","year":"2022","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_6","unstructured":"Liu, C., Yue, X., and Shi, K. (2022). Spacecraft Attitude Control: A Linear Matrix Inequality Approach, Science Press. [1st ed.]."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.actaastro.2012.12.006","article-title":"New insights on the orbital debris collision hazard at GEO","volume":"85","author":"McKnight","year":"2013","journal-title":"Acta Astronaut."},{"key":"ref_8","unstructured":"Shajiee, S. (October, January 29). Probability of collision and risk minimization of orbital debris on the Galileo satellite constellation. Proceedings of the 54th International Astronautical Congress of the International Astronautical Federation, the International Academy of Astronautics, and the International Institute of Space Law, Bremen, Germany."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1016\/j.actaastro.2018.06.036","article-title":"Space debris collision probability analysis for proposed global broadband constellations","volume":"151","author":"May","year":"2018","journal-title":"Acta Astronaut."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1504\/IJSPACESE.2017.085675","article-title":"Simulation of collision probability between space station and space debris and structure failure probability","volume":"4","author":"Liu","year":"2017","journal-title":"Int. J. Space Sci. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"83461","DOI":"10.1109\/ACCESS.2019.2922835","article-title":"Analyzing space debris flux and predicting satellites collision probability in LEO orbits based on Petri nets","volume":"7","author":"Torky","year":"2019","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/S0377-2217(02)00592-1","article-title":"On optimal inventory control with independent stochastic item returns","volume":"151","author":"Fleischmann","year":"2003","journal-title":"Eur. J. Oper. Res."},{"key":"ref_13","unstructured":"Bergamini, E., Jacobone, F., and Morea, D. (2018). Enhancing CBRNE Safety & Security: Proceedings of the SICC 2017 Conference: Science as the First Countermeasure for CBRNE and Cyber Threats, Rome, Italy, 4 October 2018, Springer International Publishing."},{"key":"ref_14","unstructured":"Johnson, L. (2013, January 25). Orbital debris: The growing threat to space operations. Proceedings of the 33rd Annual Guidance and Control Conference, Huston, TX, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1046","DOI":"10.1016\/j.asr.2007.04.081","article-title":"Instability of the present LEO satellite populations","volume":"41","author":"Johnson","year":"2008","journal-title":"Adv. Space Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.actaastro.2014.03.013","article-title":"Review of past on-orbit collisions among cataloged objects and examination of the catastrophic fragmentation concept","volume":"100","author":"Pardini","year":"2014","journal-title":"Acta Astronaut."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.actaastro.2017.01.046","article-title":"Revisiting the collision risk with cataloged objects for the Iridium and COSMO-SkyMed satellite constellations","volume":"134","author":"Pardini","year":"2017","journal-title":"Acta Astronaut."},{"key":"ref_18","first-page":"105","article-title":"Sensitivity of the space debris environment to large constellations and small satellites","volume":"70","author":"Lewis","year":"2017","journal-title":"J. Br. Interplanet. Soc."},{"key":"ref_19","unstructured":"Virgili, B., Krag, H., and Lewis, H. (2016, January 10). Mega-constellations, small satellites and their impact on the space debris environment. Proceedings of the 67th International Astronautical Congress, Guadalajara, Mexico."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.agwat.2016.12.019","article-title":"An analytical review of irrigation efficiency measured using deterministic and stochastic models","volume":"184","author":"Pereira","year":"2017","journal-title":"Agric. Water Manag."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.1287\/opre.1120.1085","article-title":"Optimizing boat resources at the US Coast Guard: Deterministic and stochastic models","volume":"60","author":"Wagner","year":"2012","journal-title":"Oper. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"956","DOI":"10.2514\/1.14254","article-title":"Design and deployment of a satellite constellation using collaborative optimization","volume":"41","author":"Budianto","year":"2004","journal-title":"J. Spacecr. Rocket."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"119","DOI":"10.2514\/1.6346","article-title":"Staged deployment of communications satellite constellations in low earth orbit","volume":"1","author":"Chaize","year":"2004","journal-title":"J. Aerosp. Comput. Inform. Commun."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"108699","DOI":"10.1016\/j.ijpe.2022.108699","article-title":"Single item periodic review inventory control with sales dependent stochastic return flows","volume":"255","year":"2023","journal-title":"Int. J. Prod. Econ."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Baeza, V., Lagunas, E., Al-Hraishawi, H., and Chatzinotas, S. (2022, January 26). An Overview of Channel Models for NGSO Satellites. Proceedings of the 2022 IEEE 96th Vehicular Technology Conference, London, UK.","DOI":"10.1109\/VTC2022-Fall57202.2022.10012693"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/5\/1024\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:29:29Z","timestamp":1760124569000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/5\/1024"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,5]]},"references-count":25,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["sym15051024"],"URL":"https:\/\/doi.org\/10.3390\/sym15051024","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,5]]}}}