{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,2]],"date-time":"2023-04-02T20:50:32Z","timestamp":1680468632103},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2012,2,23]],"date-time":"2012-02-23T00:00:00Z","timestamp":1329955200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Queueing Syst"],"published-print":{"date-parts":[[2012,4]]},"DOI":"10.1007\/s11134-012-9278-x","type":"journal-article","created":{"date-parts":[[2012,2,22]],"date-time":"2012-02-22T19:38:01Z","timestamp":1329939481000},"page":"299-337","source":"Crossref","is-referenced-by-count":4,"title":["Variational problem in the non-negative orthant of \u211d3: reflective faces and boundary influence cones"],"prefix":"10.1007","volume":"70","author":[{"given":"Ahmed","family":"El\u00a0Kharroubi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdelhak","family":"Yaacoubi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdelghani","family":"Ben\u00a0Tahar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kawtar","family":"Bichard","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,2,23]]},"reference":[{"key":"9278_CR1","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1023\/A:1011004620420","volume":"37","author":"F. Avram","year":"2001","unstructured":"Avram, F., Dai, J.G., Hasenbein, J.J.: Explicit solutions for variational problems in the quadrant. Queueing Syst. 37, 259\u2013289 (2001)","journal-title":"Queueing Syst."},{"key":"9278_CR2","doi-asserted-by":"crossref","DOI":"10.1002\/0471787779","volume-title":"Non-Linear Programming, Theory and Algorithms","author":"M. Bazaraa","year":"2006","unstructured":"Bazaraa, M., Sherali, H., Shetty, C.: Non-Linear Programming, Theory and Algorithms, 3rd edn. John Wiley & Sons, New York (2006)","edition":"3"},{"key":"9278_CR3","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1080\/17442509108833680","volume":"34","author":"A. Bernard","year":"1991","unstructured":"Bernard, A., El\u00a0Kharroubi, A.: R\u00e9gulations deterministes et stochastiques dans le\u00a0premier orthant de\u00a0\u211d n . Stoch. Stoch. Rep. 34, 149\u2013167 (1991)","journal-title":"Stoch. Stoch. Rep."},{"key":"9278_CR4","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1214\/09-AAP631","volume":"20","author":"M. Bramson","year":"2010","unstructured":"Bramson, M., Dai, J.G., Harrison, J.M.: Positive recurrence of reflecting Brownian motion in three dimensions. Ann. Appl. Probab. 20, 753\u2013783 (2010)","journal-title":"Ann. Appl. Probab."},{"issue":"5","key":"9278_CR5","doi-asserted-by":"crossref","first-page":"1686","DOI":"10.1137\/S0036139997330222","volume":"59","author":"A. Budhiraja","year":"1999","unstructured":"Budhiraja, A., Dupuis, P.: Simple necessary and sufficient conditions for the stability of constrained processes. SIAM J. Appl. Math. 59(5), 1686\u20131700 (1999)","journal-title":"SIAM J. Appl. Math."},{"key":"9278_CR6","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1214\/aop\/1176988725","volume":"22","author":"P. Dupuis","year":"1994","unstructured":"Dupuis, P., Williams, R.J.: Lyapunov functions for semimartingale reflecting Brownian motions. Ann. Probab. 22, 680\u2013702 (1994)","journal-title":"Ann. Probab."},{"issue":"2","key":"9278_CR7","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/S0304-4149(01)00151-X","volume":"98","author":"P. Dupuis","year":"2002","unstructured":"Dupuis, P., Ramanan, K.: A\u00a0time-reversed representation for the tail probabilities of stationary reflected Brownian motion. Stoch. Process. Appl. 98(2), 253\u2013288 (2002)","journal-title":"Stoch. Process. Appl."},{"key":"9278_CR8","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1080\/17442500008834224","volume":"68","author":"A. El\u00a0Kharroubi","year":"2000","unstructured":"El\u00a0Kharroubi, A., Ben\u00a0Tahar, A., Yaacoubi, A.: Sur la\u00a0r\u00e9currence positive du\u00a0mouvement Brownien r\u00e9fl\u00e9chi dans l\u2019orthant positif de\u00a0\u211d n . Stoch. Stoch. Rep. 68, 229\u2013253 (2000)","journal-title":"Stoch. Stoch. Rep."},{"key":"9278_CR9","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1007\/s001860200210","volume":"56","author":"A. El\u00a0Kharroubi","year":"2002","unstructured":"El\u00a0Kharroubi, A., Ben\u00a0Tahar, A., Yaacoubi, A.: On the stability of the linear Skorokhod problem in an orthant. Math. Methods Oper. Res. 56, 243\u2013258 (2002)","journal-title":"Math. Methods Oper. Res."},{"key":"9278_CR10","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/s11134-008-9102-9","volume":"61","author":"J.M. Harrison","year":"2009","unstructured":"Harrison, J.M., Hasenbein, J.J.: Reflected Brownian motion in the quadrant: tail behavior of the stationary distribution. Queueing Syst. 61, 113\u2013138 (2009)","journal-title":"Queueing Syst."},{"key":"9278_CR11","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1080\/17442508708833469","volume":"22","author":"J.M. Harrison","year":"1987","unstructured":"Harrison, J.M., Williams, R.J.: Brownian models of open queueing networks with homogeneous customer populations. Stochastics 22, 77\u2013115 (1987)","journal-title":"Stochastics"},{"key":"9278_CR12","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1017\/S0305004100076040","volume":"113","author":"D.G. Hobson","year":"1993","unstructured":"Hobson, D.G., Rogers, L.C.G.: Recurrence and transience of reflecting Brownian motion in the quadrant. Math. Proc. Camb. Philos. Soc. 113, 387\u2013399 (1993)","journal-title":"Math. Proc. Camb. Philos. Soc."},{"key":"9278_CR13","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1023\/A:1019148501057","volume":"29","author":"K. Majewski","year":"1998","unstructured":"Majewski, K.: Large deviation of the steady-state distribution of reflected processes with applications to queueing systems. Queueing Syst. 29, 351\u2013381 (1998)","journal-title":"Queueing Syst."},{"key":"9278_CR14","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/0024-3795(72)90019-5","volume":"5","author":"K.G. Murty","year":"1972","unstructured":"Murty, K.G.: On the number of solutions to the complementarity problem and spanning properties of complementary cones. Linear Algebra Appl. 5, 65\u2013108 (1972)","journal-title":"Linear Algebra Appl."},{"key":"9278_CR15","first-page":"805","volume":"9","author":"H. Samelson","year":"1958","unstructured":"Samelson, H., Thrall, R.M., Besler, O.: A\u00a0partition theorem for Euclidean n-space. Proc. Am. Math. Soc. 9, 805\u2013807 (1958)","journal-title":"Proc. Am. Math. Soc."},{"key":"9278_CR16","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/BF01292674","volume":"96","author":"L.M. Taylor","year":"1993","unstructured":"Taylor, L.M., Williams, R.J.: Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant. Probab. Theory Relat. Fields 96, 283\u2013317 (1993)","journal-title":"Probab. Theory Relat. Fields"},{"key":"9278_CR17","series-title":"The IMA Volumes in Mathematics and its Applications","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/978-1-4757-2418-9_7","volume-title":"Stochastic Networks","author":"R.J. Williams","year":"1995","unstructured":"Williams, R.J.: Semimartingale reflecting Brownian motions in the orthant. In: Kelly, F.P., Williams, R.J. (eds.) Stochastic Networks. The IMA Volumes in Mathematics and its Applications, vol.\u00a071, pp.\u00a0125\u2013137. Springer, New York (1995)"}],"container-title":["Queueing Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11134-012-9278-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11134-012-9278-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11134-012-9278-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T07:44:42Z","timestamp":1559375082000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11134-012-9278-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,23]]},"references-count":17,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,4]]}},"alternative-id":["9278"],"URL":"https:\/\/doi.org\/10.1007\/s11134-012-9278-x","relation":{},"ISSN":["0257-0130","1572-9443"],"issn-type":[{"value":"0257-0130","type":"print"},{"value":"1572-9443","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,2,23]]}}}