{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:29:27Z","timestamp":1760059767418,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T00:00:00Z","timestamp":1751932800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guangxi Major Science and Technology Project","award":["GuikeAA23062035-2","GuikeAA24263038","22YDPYGX00070"],"award-info":[{"award-number":["GuikeAA23062035-2","GuikeAA24263038","22YDPYGX00070"]}]},{"name":"Tianjin Science and Technology Plan Project","award":["GuikeAA23062035-2","GuikeAA24263038","22YDPYGX00070"],"award-info":[{"award-number":["GuikeAA23062035-2","GuikeAA24263038","22YDPYGX00070"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>As a key node in port logistics systems, ship anchorage is often faced with congestion caused by ship flow fluctuations, multi-priority scheduling imbalances and the poor adaptability of scheduling models to complex environments. To solve the above problems, this paper constructs a ship scheduling algorithm based on a Markov-modulated fluid priority queue, which describes the stochastic evolution of the anchorage operation state via a continuous-time Markov chain and abstracts the arrival and service processes of ships into a continuous fluid input and output mechanism modulated by the state. The algorithm introduces a multi-priority service strategy to achieve the differentiated scheduling of different types of ships and improves the computational efficiency and scalability based on a matrix analysis method. Simulation results show that the proposed model reduces the average waiting time of ships by more than 90% compared with the M\/G\/1\/1 and RL strategies and improves the utilization of anchorage resources by about 20% through dynamic service rate adjustment, showing significant advantages over traditional scheduling methods in multi-priority scenarios.<\/jats:p>","DOI":"10.3390\/a18070421","type":"journal-article","created":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T09:12:48Z","timestamp":1751965968000},"page":"421","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Ship Scheduling Algorithm Based on Markov-Modulated Fluid Priority Queues"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1401-713X","authenticated-orcid":false,"given":"Jianzhi","family":"Deng","sequence":"first","affiliation":[{"name":"College of Physics and Electronic Information Engineering, Guilin University of Technology, Guilin 541006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuilian","family":"Lv","sequence":"additional","affiliation":[{"name":"Computer Science and Engineering, Guilin University of Technology, Guilin 541006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yun","family":"Li","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic Information, Guangxi Minzu University, Nanning 530006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liping","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic Information, Guangxi Minzu University, Nanning 530006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yishan","family":"Su","sequence":"additional","affiliation":[{"name":"School of Electrical and Automation Engineering, Tianjin University, Tianjin 300074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaolin","family":"Wang","sequence":"additional","affiliation":[{"name":"Guangxi Datengxia Water Control Project Development Co., Ltd., Nanning 530021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinzhi","family":"Liu","sequence":"additional","affiliation":[{"name":"Guangxi Datengxia Water Control Project Development Co., Ltd., Nanning 530021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"109472","DOI":"10.1016\/j.cie.2023.109472","article-title":"An epsilon-constraint-based exact multi-objective optimization approach for the ship schedule recovery problem in liner shipping","volume":"183","author":"Elmi","year":"2023","journal-title":"Comput. 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