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The structure of the constraints depends on the underlying network topology. We investigate continuity and monotonicity of the resulting maximizers with respect to time. Our results have important consequences for fluid models of the corresponding networks which are optimal, in the appropriate sense, with respect to handling real-time transmission requests.<\/jats:p>","DOI":"10.1007\/s00186-020-00705-x","type":"journal-article","created":{"date-parts":[[2020,2,10]],"date-time":"2020-02-10T16:02:41Z","timestamp":1581350561000},"page":"33-76","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Continuity and monotonicity of solutions to a greedy maximization problem"],"prefix":"10.1007","volume":"92","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3073-959X","authenticated-orcid":false,"given":"\u0141ukasz","family":"Kruk","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,2,10]]},"reference":[{"key":"705_CR1","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s10479-008-0427-x","volume":"170","author":"S Aalto","year":"2009","unstructured":"Aalto S, Ayesta U (2009) SRPT applied to bandwidth sharing networks. 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