{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:31:13Z","timestamp":1760243473644,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2013,3,14]],"date-time":"2013-03-14T00:00:00Z","timestamp":1363219200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Recent advance in wireless sensor network (WSN) applications such as the Internet of Things (IoT) have attracted a lot of attention. Sensor nodes have to monitor and cooperatively pass their data, such as temperature, sound, pressure, etc. through the network under constrained physical or environmental conditions. The Quality of Service (QoS) is very sensitive to network delays. When resources are constrained and when the number of receivers increases rapidly, how the sensor network can provide good QoS (measured as  end-to-end delay) becomes a very critical problem. In this paper; a solution to the wireless sensor network multicasting problem is proposed in which a mathematical model that provides services to accommodate delay fairness for each subscriber is constructed. Granting equal consideration to both network link capacity assignment and routing strategies for each multicast group guarantees the intra-group and inter-group delay fairness of end-to-end delay. Minimizing delay and achieving fairness is ultimately achieved through the Lagrangean Relaxation method and Subgradient Optimization Technique. Test results indicate that the new system runs with greater effectiveness and efficiency.<\/jats:p>","DOI":"10.3390\/s130303588","type":"journal-article","created":{"date-parts":[[2013,3,14]],"date-time":"2013-03-14T12:22:04Z","timestamp":1363263724000},"page":"3588-3614","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Utilizing Joint Routing and Capacity Assignment Algorithms to Achieve Inter- and Intra-Group Delay Fairness in Multi-Rate Multicast Wireless Sensor Networks"],"prefix":"10.3390","volume":"13","author":[{"given":"Frank","family":"Lin","sequence":"first","affiliation":[{"name":"Department of Information Management, National Taiwan University, No. 1 Sec. 4, Roosevelt Rd., Taipei City 106, Taiwan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8475-7400","authenticated-orcid":false,"given":"Chiu-Han","family":"Hsiao","sequence":"additional","affiliation":[{"name":"Department of Information Management, National Taiwan University, No. 1 Sec. 4, Roosevelt Rd., Taipei City 106, Taiwan"}]},{"given":"Leo","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Information Management, National Taiwan University, No. 1 Sec. 4, Roosevelt Rd., Taipei City 106, Taiwan"}]},{"given":"Yean-Fu","family":"Wen","sequence":"additional","affiliation":[{"name":"Graduate Institute of Information Management, National Taipei University, No. 151, University Rd., San Shia District, New Taipei City 23741, Taiwan"}]}],"member":"1968","published-online":{"date-parts":[[2013,3,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1953","DOI":"10.1016\/j.cor.2003.12.007","article-title":"A survey of combinatorial optimization problems in multicast routing","volume":"32","author":"Oliveira","year":"2005","journal-title":"Comput. Oper. Res."},{"key":"ref_2","unstructured":"Huang, K.H. (2003). Design and Management of Efficient and Flexible Multimedia Multicast Networks. [M.Sc. Thesis, Department of Information Management, College of Management, National Taiwan University]."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1109\/65.819174","article-title":"Deployment issues for the IP multicast service and architecture","volume":"14","author":"Diot","year":"2000","journal-title":"IEEE Network"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Minoli, D. (2008). IP Multicast with Applications to IPTV and Mobile DVB-H, Wiley-IEEE Press.","DOI":"10.1002\/9780470260876"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1109\/65.752646","article-title":"An overview of quality of service routing for next-generation high-speed networks: Problems and solutions","volume":"12","author":"Chen","year":"1998","journal-title":"IEEE Network"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1109\/MCOM.2002.1007412","article-title":"Survey of QoS multicasting issues","volume":"40","author":"Striegel","year":"2002","journal-title":"IEEE Commun. Mag."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1007\/BF01386390","article-title":"A note on two problems in connexion with graphs","volume":"1","author":"Dijkstra","year":"1959","journal-title":"Numer. Math."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Coltun, R., Ferguson, D., Moy, J., and Lindem, A. (2008). RFC 5340-OSPF for IPv6; OSPFv3; The Internet Society (ISOC).","DOI":"10.17487\/rfc5340"},{"key":"ref_9","unstructured":"Chen, S., Nahrstedt, K., and Shavitt, Y. (March, January 26\u2013). A QoS-Aware Multicast Routing Protocol. Tel Aviv, Israel. Volume 3."},{"key":"ref_10","unstructured":"Khadivi, P., Samavi, S., Todd, T.D., and Saidi, H. (June, January 20\u2013). Multi-constraint QoS Routing Using a New Single Mixed Metrics. Paris, France. Volume 4."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s11134-006-7587-7","article-title":"A queueing analysis of max-min fairness, proportional fairness and balanced fairness","volume":"53","author":"Bonald","year":"2006","journal-title":"Queueing Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1006\/jcss.2001.1752","article-title":"Fairness in routing and load balancing","volume":"63","author":"Kleinberg","year":"2001","journal-title":"J. Comput. Syst. Sci."},{"key":"ref_13","unstructured":"Bertsekas, D., and Gallager, R.G. (1992). Data Networks, Upper Shaddle River. [2nd ed.]."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1057\/palgrave.jors.2600523","article-title":"Rate control for communication networks: Shadow prices, proportional fairness and stability","volume":"49","author":"Kelly","year":"1998","journal-title":"J. Oper. Res. Soc."},{"key":"ref_15","unstructured":"Jiang, L.B., and Liew, S.C. (March, January 13\u2013). Proportional Fairness in Wireless LANs and Ad Hoc Networks. New Orleans, LA, USA. Volume 3."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1016\/S0305-0548(00)00007-1","article-title":"Minimum-weight spanning tree algorithms: A survey and empirical study","volume":"28","author":"Hindi","year":"2001","journal-title":"Comput. Oper. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1145\/505241.505243","article-title":"An optimal minimum spanning tree algorithm","volume":"49","author":"Pettie","year":"2002","journal-title":"J. ACM"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1109\/MAHC.1985.10011","article-title":"On the history of the minimum spanning tree problem","volume":"7","author":"Graham","year":"1985","journal-title":"IEEE Ann. Hist. Comput."},{"key":"ref_19","unstructured":"Salama, H.F., Reeves, D.S., and Viniotis, Y. (July, January 1\u2013). The Delay-constrained Minimum Spanning Tree Problem. Alexandria, Egypt."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1287\/inte.15.2.10","article-title":"An applications oriented guide to Lagrangian Relaxation","volume":"15","author":"Fisher","year":"1985","journal-title":"Interfaces"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1007\/BFb0120690","article-title":"Lagrangean Relaxation and its uses in integer programming","volume":"2","author":"Geoffrion","year":"1974","journal-title":"Math. Program. Study"},{"key":"ref_22","unstructured":"Cheng, K.T., and Lin, F.Y.S. (November, January 13\u2013). Minimax End-to-end Delay Routing and Capacity Assignment for Virtual Circuit Networks. Singapore."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1138","DOI":"10.1287\/opre.18.6.1138","article-title":"The traveling salesman problem and minimum spanning trees: Part I","volume":"18","author":"Held","year":"1970","journal-title":"Oper. Res."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/3\/3588\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:45:32Z","timestamp":1760219132000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/3\/3588"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3,14]]},"references-count":23,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2013,3]]}},"alternative-id":["s130303588"],"URL":"https:\/\/doi.org\/10.3390\/s130303588","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2013,3,14]]}}}