{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T05:40:53Z","timestamp":1698298853011},"reference-count":16,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":4911,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1993,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this work, we compute the distribution of <jats:italic>L<\/jats:italic>*, the length of a shortest <jats:italic>(s, t)<\/jats:italic> path, in a directed network <jats:italic>G<\/jats:italic> with a source node <jats:italic>s<\/jats:italic> and a sink node <jats:italic>t<\/jats:italic> and whose arc lengths are independent, nonnegative, integer valued random variables having finite support. We construct a discrete time Markov chain with a single absorbing state and associate costs with each transition such that the total cost incurred by this chain until absorption has the same distribution as does <jats:italic>L<\/jats:italic>*. We show that the transition probability matrix of this chain has an upper triangular structure and exploit this property to develop numerically stable algorithms for computing the distribution of <jats:italic>L<\/jats:italic>* and its moments. All the algorithms are recursive in nature and are illustrated by several examples. \u00a9 <jats:italic>1993 by John Wiley &amp; Sons, Inc.<\/jats:italic><\/jats:p>","DOI":"10.1002\/net.3230230305","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T14:17:53Z","timestamp":1178979473000},"page":"175-183","source":"Crossref","is-referenced-by-count":16,"title":["Shortest paths in stochastic networks with ARC lengths having discrete distributions"],"prefix":"10.1002","volume":"23","author":[{"given":"Gehan A.","family":"Corea","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vidyadhar G.","family":"Kulkarni","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","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(66)90120-X"},{"key":"e_1_2_1_3_2","first-page":"713","article-title":"On stochastic linear programming II: Distribution problems: Non\u2010stochastic technology matrix","author":"Bereanu B.","year":"1966","journal-title":"Rev. Roumaine Math. Pures Appl."},{"key":"e_1_2_1_4_2","unstructured":"G. A.Corea Recursive methods and bounds for performance evaluation of stochastic networks. PhD Dissertation. University of North Carolina Chapel Hill NC (1989)."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01386390"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1137\/0126020"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.31.5.579"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1145\/367766.368168"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.17.4.583"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1145\/28869.28874"},{"key":"e_1_2_1_11_2","unstructured":"K. J.HayhurstandD. R.Shier A factoring approach for the stochastic shortest path problem. Technical Report No. 90\u201007. Department of Mathematics College of William and Mary Williamsburg VA (1990)."},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230160303"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.13.1.46"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/0305-0548(76)90017-4"},{"key":"e_1_2_1_15_2","unstructured":"C. E.Sigal The stochastic shortest route problem. PhD Dissertation. Purdue University West Lafayette IN (1977)."},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/0378-4754(79)90007-7"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1145\/321105.321107"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230230305","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230230305","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T13:14:39Z","timestamp":1698239679000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230230305"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,5]]},"references-count":16,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1993,5]]}},"alternative-id":["10.1002\/net.3230230305"],"URL":"https:\/\/doi.org\/10.1002\/net.3230230305","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,5]]}}}