{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T05:40:40Z","timestamp":1697866840560},"reference-count":6,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":7619,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1985,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A well known engineering principle in introducing redundancy to a system is that component\u2010level redundancy is better than system\u2010level redundancy. However, the mathematical demonstration of this principle is usually for coherent systems constructed by one sequential synthesis and one parallel synthesis (the proof consists of showing that the parallel synthesis should be at the component level). In this article we demonstrate the same principle for systems constructed by parallel\u2010sequential\u2010parallel synthesis, one parallel synthesis at the component level and one at the system level. We show that the parallel synthesis at the component level should have more redundancy. The particular vehicle we use for this demonstration is the comparison of blocking probabilities for a 2\u2010port network known as channel graphs. The crux of the mathematical demonstration is the lemma that [1 \u2212 \u03a0<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-stack-1.gif\" xlink:title=\"urn:x-wiley:00283045:media:NET3230150406:tex2gif-stack-1\" \/> (1 \u2212 <jats:italic>P<\/jats:italic><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-stack-2.gif\" xlink:title=\"urn:x-wiley:00283045:media:NET3230150406:tex2gif-stack-2\" \/>)]<jats:sup>1\/a<\/jats:sup> decreases in <jats:italic>a<\/jats:italic>, 0 \u2264 p<jats:sub>i<\/jats:sub> \u2264 1, <jats:sub>i<\/jats:sub> = 1,\u2026, <jats:italic>n<\/jats:italic>.<\/jats:p>","DOI":"10.1002\/net.3230150406","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T20:17:55Z","timestamp":1178914675000},"page":"449-453","source":"Crossref","is-referenced-by-count":1,"title":["Component\u2010level redundancy is better than system\u2010level redundancy for channel graphs"],"prefix":"10.1002","volume":"15","author":[{"given":"F. K.","family":"Hwang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L. A.","family":"Shepp","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":"10.1002\/net.3230070205"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1977.tb00570.x"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1978.tb02183.x"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1982.tb03094.x"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1977.tb00541.x"},{"key":"e_1_2_1_7_2","volume-title":"Inequalities, Theory of Majorization and Its Applications","author":"Marshall A. W.","year":"1979"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230150406","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230150406","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T20:06:41Z","timestamp":1697832401000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230150406"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1985,12]]},"references-count":6,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1985,12]]}},"alternative-id":["10.1002\/net.3230150406"],"URL":"https:\/\/doi.org\/10.1002\/net.3230150406","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1985,12]]}}}