{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,27]],"date-time":"2024-08-27T11:09:07Z","timestamp":1724756947981},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2008,7,1]],"date-time":"2008-07-01T00:00:00Z","timestamp":1214870400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2008,7]]},"abstract":"<jats:p>Both the hopcount <jats:italic>H<\/jats:italic><jats:sub><jats:italic>N<\/jats:italic><\/jats:sub> (the number of links) and the weight <jats:italic>W<\/jats:italic><jats:sub><jats:italic>N<\/jats:italic><\/jats:sub> (the sum of the weights on links) of the shortest path between two arbitrary nodes in the complete graph <jats:italic>K<\/jats:italic><jats:sub><jats:italic>N<\/jats:italic><\/jats:sub> with i.i.d. exponential link weights is computed. We consider the joint distribution of the pair (<jats:italic>H<\/jats:italic><jats:sub><jats:italic>N<\/jats:italic><\/jats:sub>, <jats:italic>W<\/jats:italic><jats:sub><jats:italic>N<\/jats:italic><\/jats:sub>) and derive, after proper scaling, the joint limiting distribution. One of the results is that <jats:italic>H<\/jats:italic><jats:sub><jats:italic>N<\/jats:italic><\/jats:sub> and <jats:italic>W<\/jats:italic><jats:sub><jats:italic>N<\/jats:italic><\/jats:sub>, properly scaled, are asymptotically independent.<\/jats:p>","DOI":"10.1017\/s0963548308009176","type":"journal-article","created":{"date-parts":[[2008,6,16]],"date-time":"2008-06-16T10:24:49Z","timestamp":1213611889000},"page":"537-548","source":"Crossref","is-referenced-by-count":4,"title":["The Weight and Hopcount of the Shortest Path in the Complete Graph with Exponential Weights"],"prefix":"10.1017","volume":"17","author":[{"given":"GERARD","family":"HOOGHIEMSTRA","sequence":"first","affiliation":[]},{"given":"PIET","family":"VAN MIEGHEM","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2008,7,1]]},"reference":[{"key":"S0963548308009176_ref1","volume-title":"Handbook of Mathematical Functions","author":"Abramowitz","year":"1968"},{"key":"S0963548308009176_ref8","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548399003892"},{"key":"S0963548308009176_ref11","doi-asserted-by":"publisher","DOI":"10.1017\/S026996480800003X"},{"key":"S0963548308009176_ref10","unstructured":"[10] Van Mieghem P. , Hooghiemstra G. and van der Hofstad R. (2000) A scaling law for the hopcount. Report, TU-Delft."},{"key":"S0963548308009176_ref7","unstructured":"[7] Hooghiemstra G. and Van Mieghem P. (2001) Delay distributions on fixed internet paths. Delft University of Technology, report 20011020. www.nas.ewi.tudelft.nl\/people\/Piet\/TUDelftreports"},{"key":"S0963548308009176_ref3","volume-title":"The Asymptotic Theory of Extreme Order Statistics","author":"Galambos","year":"1987"},{"key":"S0963548308009176_ref4","doi-asserted-by":"publisher","DOI":"10.1017\/S026996480115206X"},{"key":"S0963548308009176_ref5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022175620150"},{"key":"S0963548308009176_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511616488"},{"key":"S0963548308009176_ref2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511608834"},{"key":"S0963548308009176_ref6","first-page":"1","article-title":"The size and the weight of the shortest path trees with exponential link weights","volume":"16","author":"van der Hofstad","year":"2006","journal-title":"Combin. Probab. Comput."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548308009176","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,5]],"date-time":"2019-04-05T19:19:11Z","timestamp":1554491951000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548308009176\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,7]]},"references-count":11,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,7]]}},"alternative-id":["S0963548308009176"],"URL":"https:\/\/doi.org\/10.1017\/s0963548308009176","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,7]]}}}