{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T20:32:46Z","timestamp":1648845166470},"reference-count":21,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>In many systems such as computer network, fuel distribution, and transportation system, it is necessary to change the capacity of some arcs in order to increase maximum flow value from source<jats:italic>s<\/jats:italic>to sink<jats:italic>t<\/jats:italic>, while the capacity change incurs minimum cost. In real-time networks, some factors cause loss of arc\u2019s flow. For example, in some flow distribution systems, evaporation, erosion or sediment in pipes waste the flow. Here we define a real capacity, or the so-called<jats:italic>functional capacity,<\/jats:italic>which is the operational capacity of an arc. In other words, the functional capacity of an arc equals the possible maximum flow that may pass through the arc. Increasing the functional arcs capacities incurs some cost. There is a certain resource available to cover the costs. First, we construct a mathematical model to minimize the total cost of expanding the functional capacities to the required levels. Then, we consider the loss of flow on each arc as a stochastic variable and compute the system reliability.<\/jats:p>","DOI":"10.1155\/2014\/876260","type":"journal-article","created":{"date-parts":[[2014,8,19]],"date-time":"2014-08-19T21:21:29Z","timestamp":1408483289000},"page":"1-9","source":"Crossref","is-referenced-by-count":0,"title":["Capacity Expansion and Reliability Evaluation on the Networks Flows with Continuous Stochastic Functional Capacity"],"prefix":"10.1155","volume":"2014","author":[{"given":"F.","family":"Hamzezadeh","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Basic Science, Karaj Branch, Islamic Azad University, Alborz, Karaj 31485-313, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H.","family":"Salehi Fathabadi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Basic Science, Karaj Branch, Islamic Azad University, Alborz, Karaj 31485-313, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"issue":"3","key":"1","first-page":"399","volume":"8","year":"1956","journal-title":"Canadian Journal of Mathematics"},{"key":"2","first-page":"434","volume":"15","year":"1974","journal-title":"Soviet Mathematics Doklady"},{"issue":"2","key":"3","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1002\/net.3230250207","volume":"25","year":"1995","journal-title":"Networks"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(90)90024-R"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1287\/opre.37.5.748"},{"key":"6","first-page":"1168","volume":"54","year":"2012","journal-title":"Social and Behavioral Sciences"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01719791"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(96)90072-7"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/S0951-8320(00)00070-3"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/327078"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2009.05.016"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.omega.2004.04.005"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1504\/IJMOR.2012.048904"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2010.11.002"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/S0305-0548(02)00094-1"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1023\/A:1007536520393"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/0951-8320(88)90122-6"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1109\/TR.1986.4335422"},{"key":"19","year":"1993"},{"key":"20","year":"1984"},{"key":"21","year":"1974"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/876260.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/876260.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/876260.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T18:59:29Z","timestamp":1498157969000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/876260\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":21,"alternative-id":["876260","876260"],"URL":"https:\/\/doi.org\/10.1155\/2014\/876260","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}