{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T19:57:12Z","timestamp":1771703832934,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2011,3,25]],"date-time":"2011-03-25T00:00:00Z","timestamp":1301011200000},"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>In this paper, we propose a solution to the problem of guaranteed time slot allocation in cluster-tree WSNs. Our design uses the so-called Network Utility Maximization (NUM) approach as far as we aim to provide a fair distribution of the available resources. From the point of view of implementation, we extend here the authors\u2019 proposed Coupled-Decompositions Method (CDM) in order to compute the NUM problem inside the cluster tree topology and we prove the optimality of this new extended version of the method. As a result, we obtain a distributed solution that reduces the total amount of signalling information in the network up to a factor of 500 with respect to the classical techniques, that is, primal and dual decomposition. This is possible because the CDM finds the optimal solution with a small number of iterations. Furthermore, when we compare our solution to the standard-proposed First Come First Serve (FCFS) policy, we realize that FCFS becomes pretty unfair as the traffic load in the network increases and thus, a fair allocation of resources can be considered whenever the price to pay in terms of signalling and computational complexity is controlled.<\/jats:p>","DOI":"10.3390\/s110403611","type":"journal-article","created":{"date-parts":[[2011,3,25]],"date-time":"2011-03-25T11:14:25Z","timestamp":1301051665000},"page":"3611-3639","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optimal Rate Allocation in Cluster-Tree WSNs"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2249-8594","authenticated-orcid":false,"given":"Antoni","family":"Morell","sequence":"first","affiliation":[{"name":"Telecommunications and Systems Engineering Department, Universitat Aut\u00f2noma de Barcelona, UAB Campus, 08193 Cerdanyola del Vall`es, Spain"}]},{"given":"Jose Lopez","family":"Vicario","sequence":"additional","affiliation":[{"name":"Telecommunications and Systems Engineering Department, Universitat Aut\u00f2noma de Barcelona, UAB Campus, 08193 Cerdanyola del Vall`es, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3020-427X","authenticated-orcid":false,"given":"Xavier","family":"Vilajosana","sequence":"additional","affiliation":[{"name":"IT, Multimedia and Telecommunications Department, Universitat Oberta de Catalunya, Rambla Poblenou, 156, 08018 Barcelona, Spain"}]},{"given":"Ignasi","family":"Vilajosana","sequence":"additional","affiliation":[{"name":"World Sensing S.L., Baixada Gomis, 1, 08023 Barcelona, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2494-6872","authenticated-orcid":false,"given":"Gonzalo","family":"Seco-Granados","sequence":"additional","affiliation":[{"name":"Telecommunications and Systems Engineering Department, Universitat Aut\u00f2noma de Barcelona, UAB Campus, 08193 Cerdanyola del Vall`es, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2011,3,25]]},"reference":[{"key":"ref_1","unstructured":"IEEE (2006). 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