{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:57:15Z","timestamp":1760241435639,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,2,17]],"date-time":"2018-02-17T00:00:00Z","timestamp":1518825600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this work, a multi-hop string network with a single sink node is analyzed. A periodic optimal scheduling for TDMA operation that considers the characteristic long propagation delay of the underwater acoustic channel is presented. This planning of transmissions is obtained with the help of a new geometrical method based on a 2D lattice in the space-time domain. In order to evaluate the performance of this optimal scheduling, two service policies have been compared: FIFO and Round-Robin. Simulation results, including achievable throughput, packet delay, and queue length, are shown. The network fairness has also been quantified with the Gini index.<\/jats:p>","DOI":"10.3390\/s18020612","type":"journal-article","created":{"date-parts":[[2018,2,20]],"date-time":"2018-02-20T03:54:22Z","timestamp":1519098862000},"page":"612","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Optimal Scheduling and Fair Service Policy for STDMA in Underwater Networks with Acoustic Communications"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9287-2329","authenticated-orcid":false,"given":"Miguel-\u00c1ngel","family":"Luque-Nieto","sequence":"first","affiliation":[{"name":"Department of Ingenier\u00eda de Comunicaciones, University of M\u00e1laga, M\u00e1laga 29010, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5023-2350","authenticated-orcid":false,"given":"Jos\u00e9-Miguel","family":"Moreno-Rold\u00e1n","sequence":"additional","affiliation":[{"name":"Department of Ingenier\u00eda de Comunicaciones, University of M\u00e1laga, M\u00e1laga 29010, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3042-4392","authenticated-orcid":false,"given":"Pablo","family":"Otero","sequence":"additional","affiliation":[{"name":"Department of Ingenier\u00eda de Comunicaciones, University of M\u00e1laga, M\u00e1laga 29010, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5024-8843","authenticated-orcid":false,"given":"Javier","family":"Poncela","sequence":"additional","affiliation":[{"name":"Department of Ingenier\u00eda de Comunicaciones, University of M\u00e1laga, M\u00e1laga 29010, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2018,2,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Saini, J., and Dixit, B.K. (2016). Prospects and Challenges of Underwater Acoustic Sensor Networking: A review. Indian J. Sci. Technol., 9.","DOI":"10.17485\/ijst\/2016\/v9i36\/73476"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Xiao, Y. (2010). Research Challenges in Communication protocol design for underwater Sensor networks. Underwater Acoustic Sensor Networks, Auerbach Publications.","DOI":"10.1201\/9781420067125"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/j.adhoc.2005.01.004","article-title":"Underwater acoustic networks: research challenges","volume":"3","author":"Akyildiz","year":"2005","journal-title":"Ad Hoc Netw."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Luque-Nieto, M.A., Moreno-Rold\u00e1n, J.M., Poncela, J., and Otero, P. (2016). Optimal Fair Scheduling in S-TDMA Sensor Networks for Monitoring River Plumes. J. Sens.","DOI":"10.1155\/2016\/8671516"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1109\/JOE.2013.2291135","article-title":"Underwater Optical Wireless Networks: A k-Connectivity Analysis","volume":"39","author":"Vavoulas","year":"2014","journal-title":"IEEE J. Oceanic Eng."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Anjangi, P., and Chitre, M. (2015, January 22\u201324). Design and Implementation of Super-TDMA: A MAC Protocol Exploiting Large Propagation Delays for Underwater Acoustic Networks. Proceedings of the 10th ACM International Conferences on Underwater Networks & Systems (WUWNet\u201915), Washington, DC, USA.","DOI":"10.1145\/2831296.2831299"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1433","DOI":"10.1109\/SURV.2014.013014.00032","article-title":"A survey on MAC protocols for underwater wireless sensor networks","volume":"16","author":"Chen","year":"2014","journal-title":"IEEE Commun. Surv. Tutorials"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.jnca.2017.01.030","article-title":"Performance comparison of TDMA variants for underwater acoustic sensor networks","volume":"92","author":"Mandal","year":"2017","journal-title":"J. Netw. Comput. Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1049\/ip-rsn:20045060","article-title":"ACMENet: An Underwater Acoustic Sensor Network Protocol for Real-time Environmental Monitoring in Coastal Areas","volume":"153","author":"Adams","year":"2006","journal-title":"IEE Proc. Radar Sonar Navig."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"501","DOI":"10.3390\/s100100501","article-title":"SBMAC: Smart Blocking MAC Mechanism for Variable UW-ASN (Underwater Acoustic Sensor Network) Environment","volume":"10","author":"Shin","year":"2010","journal-title":"Sensors"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Hsu, C.-C., Lai, K.-F., Chou, C.-F., and Lin, K.-J. (2009, January 19\u201325). ST-MAC: Spatial Temporal MAC Scheduling for Underwater Sensor Networks. Proceedings of the IEEE International Conference on Computer Communications (INFOCOM\u201909), Rio de Janeiro, Brazil.","DOI":"10.1109\/INFCOM.2009.5062103"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"934","DOI":"10.1109\/TCOM.1985.1096405","article-title":"Spatial TDMA: A collision free multihop channel access protocol","volume":"33","author":"Nelson","year":"1985","journal-title":"IEEE Trans. Commun."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1109\/JOE.2012.2203060","article-title":"Throughput of networks with large propagation delays","volume":"37","author":"Chitre","year":"2012","journal-title":"IEEE J. Oceanic Eng."},{"key":"ref_14","unstructured":"Anjangi, P., and Chitre, M. (September, January 30). Experimental Demonstration of Super-TDMA: A MAC Protocol Exploiting Large Propagation Delays in Underwater Acoustic Networks. Proceedings of the 3rd Underwater Communications and Networking Conference (UComms\u201916), Lerici, Italy."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1109\/JOE.2015.2474455","article-title":"Throughput-Maximizing Transmission Schedules for Underwater Acoustic Multihop Grid Networks","volume":"40","author":"Lmai","year":"2015","journal-title":"IEEE J. Oceanic Eng."},{"key":"ref_16","first-page":"156","article-title":"Throughput-Efficient Super-TDMA MAC Transmission Schedules in Ad Hoc Linear Underwater Acoustic Networks","volume":"42","author":"Lmai","year":"2017","journal-title":"IEEE J. Oceanic Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"961","DOI":"10.1109\/JOE.2010.2055271","article-title":"Analysis of a Linear Multihop Underwater Acoustic Network","volume":"35","author":"Zhang","year":"2010","journal-title":"IEEE J. Oceanic Eng."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Ali, B., Sher, A., Javaid, N., Islam, S., Aurangzeb, K., and Haider, S.I. (2018). Retransmission Avoidance for Reliable Data Delivery in Underwater WSNs. Sensors, 18.","DOI":"10.3390\/s18010149"},{"key":"ref_19","unstructured":"Hennessy, M. (1988). Algebraic Theory of Processes, MIT Press."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Cerone, A., and Hennessy, M. (2013). Modelling Probabilistic Wireless Networks. Logical Methods Comput. Sci., 9.","DOI":"10.2168\/LMCS-9(3:26)2013"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"6585","DOI":"10.1016\/j.tcs.2011.07.016","article-title":"A timed calculus for wireless systems","volume":"412","author":"Merro","year":"2011","journal-title":"Theor. Comput. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Bugliesi, M., Gallina, L., Marin, A., Rossi, S., and Hamadou, S. (2012, January 17\u201320). Interference-Sensitive Preorders for MANETs. Proceedings of the 2012 Ninth International Conference on Quantitative Evaluation of Systems (QEST), London, UK.","DOI":"10.1109\/QEST.2012.15"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Gallina, L., Marin, A., Rossi, S., Han, T., and Kwiatowska, M. (2013, January 3\u20138). A process algebraic framework for estimating the energy consumption in ad-hoc wireless sensor networks. Proceedings of the 16th ACM International Conference on Modeling, Analysis & Simulation of Wireless and Mobile Systems (MSWiM\u201913), Barcelona, Spain.","DOI":"10.1145\/2507924.2507958"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Gross, D., Shortle, J.F., Thompson, J.M., and Harris, C.M. (2008). Fundamentals of Queueing Theory, John Wiley & Sons. [4th ed.].","DOI":"10.1002\/9781118625651"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Kredo, K., Djukic, P., and Mohapatra, P. (2009, January 19\u201325). STUMP: Exploiting position diversity in the staggered TDMA underwater MAC protocol. Proceedings of the IEEE International Conference on Computer Communications (INFOCOM\u201909), Rio de Janeiro, Brazil.","DOI":"10.1109\/INFCOM.2009.5062267"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1454","DOI":"10.1109\/26.61386","article-title":"A single-server queue with vacations and gated time-limited service","volume":"38","author":"Leung","year":"1990","journal-title":"IEEE Trans. Commun."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Alfa, A.S. (2010). Queueing Theory for Telecommunications: Discrete Time Modelling of a Single Node System, Springer Science & Business Media.","DOI":"10.1007\/978-1-4419-7314-6"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1109\/90.879343","article-title":"Fair end-to-end window-based congestion control","volume":"8","author":"Mo","year":"2000","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1535","DOI":"10.1002\/dac.2416","article-title":"A fairness adaptive TDMA scheduling algorithm for wireless sensor networks with unreliable links","volume":"27","author":"Wang","year":"2014","journal-title":"Int. J. Commun. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1109\/JOE.2011.2107950","article-title":"Spatial reuse time-division multiple access for broadcast ad hoc underwater acoustic communication networks","volume":"36","author":"Diamant","year":"2011","journal-title":"IEEE J. Oceanic Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1538","DOI":"10.1109\/TMC.2011.190","article-title":"Tight performance bounds of multihop fair access for MAC protocols in wireless sensor networks and underwater sensor networks","volume":"11","author":"Xiao","year":"2012","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_32","unstructured":"Gini, C. (1912). Variabilit\u00e0 e Mutuabilit\u00e0. Contributo allo Studio delle Distribuzioni e delle Relazioni Statistiche, Tipografia di Paolo Cuppini."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"124","DOI":"10.2307\/2223319","article-title":"Measurement of inequality of incomes","volume":"31","author":"Gini","year":"1921","journal-title":"Econ. J."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/0304-3878(88)90002-8","article-title":"Migration, remittances and inequality: A sensitivity analysis using the extended Gini index","volume":"28","author":"Stark","year":"1988","journal-title":"J. Dev Econ."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"5773","DOI":"10.1021\/jm070562u","article-title":"Gini coefficient: A new way to express selectivity of kinase inhibitors against a family of kinases","volume":"50","author":"Graczyk","year":"2007","journal-title":"J. Med. Chem."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1016\/j.compeleceng.2011.12.001","article-title":"Joint scheduling and routing algorithm with load balancing in wireless mesh network","volume":"38","author":"Ning","year":"2012","journal-title":"Comput. Electr. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"306","DOI":"10.2307\/1937992","article-title":"The estimation of the Lorenz curve and Gini index","volume":"54","author":"Gastwirth","year":"1972","journal-title":"Rev. Econ. Stat."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/2\/612\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:55:28Z","timestamp":1760194528000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/2\/612"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,17]]},"references-count":37,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,2]]}},"alternative-id":["s18020612"],"URL":"https:\/\/doi.org\/10.3390\/s18020612","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2018,2,17]]}}}