{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,23]],"date-time":"2023-11-23T08:55:29Z","timestamp":1700729729255},"reference-count":19,"publisher":"Wiley","issue":"7","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":4758,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1993,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Consider a flow network whose nodes do not restrict flow transmission and arcs have random, discrete, and independent capacities. Let <jats:italic>s<\/jats:italic> and <jats:italic>t<\/jats:italic> be a pair of selected nodes, let \u03b4 denote the value of a maximum <jats:italic>s<\/jats:italic>\u2014<jats:italic>t<\/jats:italic> flow, and let \u0393 denote a set of <jats:italic>s<\/jats:italic>\u2013<jats:italic>t<\/jats:italic> cuts. Also, let \u2131 denote a set of independent joint capacity distributions with common state space. For fixed <jats:italic>l<\/jats:italic> &lt; <jats:italic>u<\/jats:italic>, this paper develops methods for approximating the probability that <jats:italic>l<\/jats:italic> \u2264 \u0394 &lt; <jats:italic>u<\/jats:italic> and the probability that a cut in \u0393 is minimum given that <jats:italic>l<\/jats:italic> \u2264 \u03b4 &lt; <jats:italic>u<\/jats:italic> for each distribution in \u2131. Since these evaluations are NP\u2010hard problems, it shows how information obtained during an iterative procedure for computing the probability that <jats:italic>l<\/jats:italic> \u2264 \u03b4 &lt; <jats:italic>u<\/jats:italic> can be used for designing an efficient Monte Carlo sampling plan that performs sampling at few capacity distributions and uses sampling data to estimate the probabilities of interest at each distribution in \u2131. The set of sampling distributions is chosen by solving an uncapacitated facility location problem. The paper also describes techniques for computing confidence intervals and includes an algorithm for implementing the sampling experiment. An example illustrates the efficiency of the proposed method. This method is applicable to the computation of performance measures for networks whose elements have discrete random weights (lengths, gains, etc.) for a set of joint weight distributions with common state space. \u00a9 <jats:italic>1993 by John Wiley &amp; Sons, Inc.<\/jats:italic><\/jats:p>","DOI":"10.1002\/net.3230230704","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T16:49:15Z","timestamp":1178988555000},"page":"605-621","source":"Crossref","is-referenced-by-count":8,"title":["Sensitivity analysis in stochastic flow networks using the Monte Carlo method"],"prefix":"10.1002","volume":"23","author":[{"given":"Christos","family":"Alexopoulos","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"George S.","family":"Fishman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"C.Alexopoulos Maximum flows and critical cutsets in stochastic networks with discrete arc capacities. Ph.D. Thesis Department of Operations Research University of North Carolina at Chapel Hill (1988)."},{"key":"e_1_2_1_3_2","unstructured":"C.Alexopoulos Distribution\u2010free confidence intervals for conditional probabilities and ratios of expectations. Technical Report School of Industrial and Systems Engineering Georgia Institute of Technology (1990; revised August1993)."},{"key":"e_1_2_1_4_2","unstructured":"C.Alexopoulos Computing criticality indices of arcs and the mean maximum flow value in networks with discrete random capacities. Technical Report School of Industrial and Systems Engineering Georgia Institute of Technology (1993)."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230210706"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/TR.1986.4335422"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.1982.4308860"},{"key":"e_1_2_1_8_2","volume-title":"Discrete Location Theory","author":"Cornuejols G.","year":"1990"},{"key":"e_1_2_1_9_2","first-page":"45","article-title":"Transportation networks with random arc capacities","volume":"3","author":"Doulliez P.","year":"1972","journal-title":"R.A.I.R.O."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230060208"},{"key":"e_1_2_1_11_2","volume-title":"Principles of Discrete Event Simulation","author":"Fishman G. S.","year":"1978"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-7152(91)90082-3"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0269964800002011"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.2307\/2683661"},{"key":"e_1_2_1_15_2","volume-title":"Communication, Transmission and Transportation Networks","author":"Frank H.","year":"1971"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02288321"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1137\/0208012"},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/0377-2217(89)90189-6"},{"key":"e_1_2_1_19_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8122-8"},{"key":"e_1_2_1_20_2","volume-title":"Combinatorial Optimization: Algorithms and Complexity","author":"Papadimitriou C.","year":"1982"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230230704","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230230704","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T21:45:32Z","timestamp":1698183932000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230230704"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,10]]},"references-count":19,"journal-issue":{"issue":"7","published-print":{"date-parts":[[1993,10]]}},"alternative-id":["10.1002\/net.3230230704"],"URL":"https:\/\/doi.org\/10.1002\/net.3230230704","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,10]]}}}