{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,17]],"date-time":"2023-11-17T19:55:27Z","timestamp":1700250927596},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2010,9,17]],"date-time":"2010-09-17T00:00:00Z","timestamp":1284681600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math Meth Oper Res"],"published-print":{"date-parts":[[2010,12]]},"DOI":"10.1007\/s00186-010-0329-y","type":"journal-article","created":{"date-parts":[[2010,9,15]],"date-time":"2010-09-15T19:44:18Z","timestamp":1284579858000},"page":"477-499","source":"Crossref","is-referenced-by-count":3,"title":["State space collapse and stability of queueing networks"],"prefix":"10.1007","volume":"72","author":[{"given":"Rosario","family":"Delgado","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2010,9,17]]},"reference":[{"key":"329_CR1","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1080\/17442509108833680","volume":"34","author":"A Bernard","year":"1991","unstructured":"Bernard A, el Kharroubi A (1991) R\u00e9gulations d\u00e9terministes et stochastiques dans le premier orthant de $${\\mathbb{R}^n}$$ . Stoch Stoch Rep 34: 149\u2013167","journal-title":"Stoch Stoch Rep"},{"key":"329_CR2","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/BF01159391","volume":"22","author":"M Bramson","year":"1996","unstructured":"Bramson M (1996) Convergence to equilibria for fluid models of FIFO queueing networks. Queueing Syst 22: 5\u201345","journal-title":"Queueing Syst"},{"key":"329_CR3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01206549","volume":"23","author":"M Bramson","year":"1996","unstructured":"Bramson M (1996) Convergence to equilibria for fluid models of head-of-the-line proportional processor sharing queueing networks. Queueing Syst 23: 1\u201326","journal-title":"Queueing Syst"},{"key":"329_CR4","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1023\/A:1019182619288","volume":"28","author":"M Bramson","year":"1998","unstructured":"Bramson M (1998) Stability of two families of queueing networks and a discussion of fluid limits. Queueing Syst 28: 7\u201331","journal-title":"Queueing Syst"},{"key":"329_CR5","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1023\/A:1019160803783","volume":"30","author":"M Bramson","year":"1998","unstructured":"Bramson M (1998) State space collapse with application to heavy traffic limits for multi-class queueing networks. Queueing Syst 30: 89\u2013148","journal-title":"Queueing Syst"},{"key":"329_CR6","unstructured":"Bramson M (2008) Stability of queueing networks. Lecture Notes in Mathematics 1950, \u00c9cole d\u2019\u00c9t\u00e9 de Probabilit\u00e9s de Saint-Flour XXXVI-2006, Springer"},{"issue":"1","key":"329_CR7","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1214\/aoap\/998926987","volume":"11","author":"M Bramson","year":"2001","unstructured":"Bramson M, Dai JG (2001) Heavy traffic limits for some queueing networks. Ann Appl Prob 11(1): 49\u201390","journal-title":"Ann Appl Prob"},{"issue":"3","key":"329_CR8","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1214\/aoap\/1177004699","volume":"5","author":"H Chen","year":"1995","unstructured":"Chen H (1995) Fluid approximations and stability of multiclass queueing networks: work-conserving disciplines. Ann Appl Prob 5(3): 637\u2013665","journal-title":"Ann Appl Prob"},{"issue":"1","key":"329_CR9","doi-asserted-by":"crossref","first-page":"026","DOI":"10.1287\/opre.48.1.26.12456","volume":"48","author":"H Chen","year":"2000","unstructured":"Chen H, Zhang H (2000) Stability of multiclass queueing networks under priority service disciplines. Oper Res 48(1): 026\u2013037","journal-title":"Oper Res"},{"issue":"1","key":"329_CR10","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1214\/aoap\/1177004828","volume":"5","author":"JG Dai","year":"1995","unstructured":"Dai JG (1995) On positive Harris recurrence of multiclass queueing networks: a unified approach via fluid limit models. Ann Appl Prob 5(1): 49\u201377","journal-title":"Ann Appl Prob"},{"issue":"11","key":"329_CR11","doi-asserted-by":"crossref","first-page":"1889","DOI":"10.1109\/9.471210","volume":"40","author":"JG Dai","year":"1995","unstructured":"Dai JG, Meyn SP (1995) Stability and convergence of moments for multiclass queueing networks via fluid limit models. IEEE Trans Aut Cont 40(11): 1889\u20131904","journal-title":"IEEE Trans Aut Cont"},{"key":"329_CR12","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/s11134-008-9080-y","volume":"59","author":"R Delgado","year":"2008","unstructured":"Delgado R (2008) State space collapse for asymptotically critical multi-class fluid networks. Queueing Syst 59: 157\u2013184","journal-title":"Queueing Syst"},{"issue":"53","key":"329_CR13","first-page":"117","volume":"52","author":"N El Karoui","year":"1978","unstructured":"El Karoui N, Chaleyat-Maurel M (1978) Un probl\u00e8me de r\u00e9flexion et ses aplications au temps local et aux \u00e9quations diff\u00e9rentielles stochastiques sur $${\\mathbb R}$$ . Cas continu, Soci\u00e9t\u00e9 Math\u00e9matique de France, Ast\u00e9risque 52(53): 117\u2013144","journal-title":"Cas continu, Soci\u00e9t\u00e9 Math\u00e9matique de France, Ast\u00e9risque"},{"key":"329_CR14","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1287\/opre.5.4.518","volume":"5","author":"JR Jackson","year":"1957","unstructured":"Jackson JR (1957) Networks of waiting lines. Oper Res 5: 518\u2013521","journal-title":"Oper Res"},{"key":"329_CR15","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1214\/aoap\/1177005204","volume":"4","author":"SP Meyn","year":"1994","unstructured":"Meyn SP, Tweedie RL (1994) State-dependent criteria for convergence of Markov chains. Ann Appl Probab 4: 149\u2013168","journal-title":"Ann Appl Probab"},{"key":"329_CR16","doi-asserted-by":"crossref","unstructured":"Reiman MI (1984) Some diffusion approximations with state space collapse. In: Baccelli F, Fayolle G (eds) Proceedings of the internat. Seminar on modeling and performance evaluation methodology, lecture notes in control and information sciences, pp 209\u2013240","DOI":"10.1007\/BFb0005175"},{"key":"329_CR17","first-page":"2","volume":"28","author":"AN Rybko","year":"1992","unstructured":"Rybko AN, Stolyar AL (1992) Ergodicity of stochastic processes describing the operations of open queueing networks. Probl Peredachi Inf 28: 2\u201326","journal-title":"Probl Peredachi Inf"},{"key":"329_CR18","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/s10479-007-0303-0","volume":"160","author":"J Tang","year":"2008","unstructured":"Tang J, Zhao YQ (2008) Stationary tail asymptotics of a tandem queue with feedback. Ann Oper Res 160: 173\u2013189","journal-title":"Ann Oper Res"},{"key":"329_CR19","doi-asserted-by":"crossref","first-page":"74","DOI":"10.2307\/3211839","volume":"8","author":"W Whitt","year":"1971","unstructured":"Whitt W (1971) Weak convergence theorems for priority queues: preemptive resume discipline. J Appl Prob 8: 74\u201394","journal-title":"J Appl Prob"},{"key":"329_CR20","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1019156702875","volume":"30","author":"RJ Williams","year":"1998","unstructured":"Williams RJ (1998) An invariance principle for semimartingale reflecting Brownian motions in an orthant. Queueing Syst 30: 5\u201325","journal-title":"Queueing Syst"},{"key":"329_CR21","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1023\/A:1019108819713","volume":"30","author":"RJ Williams","year":"1998","unstructured":"Williams RJ (1998) Diffusion approximations for open multi-class queueing networks: sufficient conditions involving state space collapse. Queueing Syst 30: 27\u201388","journal-title":"Queueing Syst"}],"container-title":["Mathematical Methods of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-010-0329-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00186-010-0329-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-010-0329-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T10:33:29Z","timestamp":1558607609000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00186-010-0329-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9,17]]},"references-count":21,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,12]]}},"alternative-id":["329"],"URL":"https:\/\/doi.org\/10.1007\/s00186-010-0329-y","relation":{},"ISSN":["1432-2994","1432-5217"],"issn-type":[{"value":"1432-2994","type":"print"},{"value":"1432-5217","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,9,17]]}}}