{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T12:35:54Z","timestamp":1759667754927},"reference-count":23,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"National Security Agency, USA","award":["H 98230-11-1-0184","64349-0042"],"award-info":[{"award-number":["H 98230-11-1-0184","64349-0042"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Operations Research"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>We consider two parallel queues, each with independent Poisson arrival rates, that are tended by a single server. The exponential server devotes all of its capacity to the longer of the queues. If both queues are of equal length, the server devotes<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>\u03bd<\/mml:mi><\/mml:mrow><\/mml:math>of its capacity to the first queue and the remaining<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mn>1<\/mml:mn><mml:mo>\u2212<\/mml:mo><mml:mi>\u03bd<\/mml:mi><\/mml:math>to the second. We obtain exact integral representations for the joint probability distribution of the number of customers in this two-node network. Then we evaluate this distribution in various asymptotic limits, such as large numbers of customers in either\/both of the queues, light traffic where arrivals are infrequent, and heavy traffic where the system is nearly unstable.<\/jats:p>","DOI":"10.1155\/2013\/680539","type":"journal-article","created":{"date-parts":[[2013,5,13]],"date-time":"2013-05-13T17:04:15Z","timestamp":1368464655000},"page":"1-21","source":"Crossref","is-referenced-by-count":2,"title":["On the Nonsymmetric Longer Queue Model: Joint Distribution, Asymptotic Properties, and Heavy Traffic Limits"],"prefix":"10.1155","volume":"2013","author":[{"given":"Charles","family":"Knessl","sequence":"first","affiliation":[{"name":"Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60607-7045, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haishen","family":"Yao","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, QCC, The City University of New York, 222-05 56th Avenue, Bayside, NY 11364, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"key":"12","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1017\/S0269964800001376","volume":"3","year":"1989","journal-title":"Probability in the Engineering and Informational Sciences"},{"key":"23","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1287\/opre.38.2.296","volume":"38","year":"1990","journal-title":"Operations Research"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01158902"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160300206"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1080\/15326349908807169"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02412240"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1137\/0144074"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1137\/0145052"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/BF00535168"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.2307\/3213071"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1091543429"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1007\/s11134-010-9197-7"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01189045"},{"key":"7","series-title":"North-Holland Mathematics Studies","first-page":"xii+405","volume":"79","year":"1983"},{"key":"9","first-page":"xvi+156","volume":"40","year":"1999"},{"key":"18","first-page":"447","year":"1992"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719260"},{"key":"4","first-page":"xvi+425","year":"1986"},{"key":"3","first-page":"xiv+593","year":"1978"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511801655"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032770"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9590.2007.00399.x"},{"key":"22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4236\/am.2011.21001","volume":"2","year":"2011","journal-title":"Progress in Applied Mathematics"}],"container-title":["Advances in Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/aor\/2013\/680539.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/aor\/2013\/680539.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/aor\/2013\/680539.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T08:57:08Z","timestamp":1498035428000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/aor\/2013\/680539\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":23,"alternative-id":["680539","680539"],"URL":"https:\/\/doi.org\/10.1155\/2013\/680539","relation":{},"ISSN":["1687-9147","1687-9155"],"issn-type":[{"value":"1687-9147","type":"print"},{"value":"1687-9155","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}