{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,15]],"date-time":"2025-08-15T00:36:06Z","timestamp":1755218166009,"version":"3.43.0"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2000,12,1]],"date-time":"2000-12-01T00:00:00Z","timestamp":975628800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2000,12,1]],"date-time":"2000-12-01T00:00:00Z","timestamp":975628800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Queueing Systems"],"published-print":{"date-parts":[[2000,12]]},"DOI":"10.1023\/a:1011037419624","type":"journal-article","created":{"date-parts":[[2003,2,19]],"date-time":"2003-02-19T17:07:13Z","timestamp":1045674433000},"page":"327-349","source":"Crossref","is-referenced-by-count":26,"title":["A Multiclass Feedback Queueing Network with a Regular Skorokhod Problem"],"prefix":"10.1007","volume":"36","author":[{"given":"Paul","family":"Dupuis","sequence":"first","affiliation":[]},{"given":"Kavita","family":"Ramanan","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"313798_CR1","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/S0304-4149(99)00051-4","volume":"84","author":"R. Atar","year":"1999","unstructured":"R. Atar and P. Dupuis, Large deviations and queueing networks: methods for rate function identification, Stochastic Process. Appl. 84 (1999) 255\u2013296.","journal-title":"Stochastic Process. Appl."},{"key":"313798_CR2","volume-title":"Nonnegative Matrices in the Mathematical Sciences","author":"A. Berman","year":"1979","unstructured":"A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences (Academic Press, New York, 1979)."},{"key":"313798_CR3","first-page":"149","volume":"34","author":"A. Bernard","year":"1991","unstructured":"A. Bernard and A. El Kharroubi, Regulations de processus dans le premier \u201corthant\u201d de \u211dn, Stochastics 34 (1991) 149\u2013167.","journal-title":"Stochastics"},{"key":"313798_CR4","doi-asserted-by":"crossref","first-page":"1686","DOI":"10.1137\/S0036139997330222","volume":"59","author":"A. Budhiraja","year":"1999","unstructured":"A. Budhiraja and P. Dupuis, Simple necessary and sufficient conditions for the stability of constrained processes, SIAM J. Appl. Math. 59 (1999) 1686\u20131700.","journal-title":"SIAM J. Appl. Math."},{"key":"313798_CR5","first-page":"1436","volume":"19","author":"H. Chen","year":"1991","unstructured":"H. Chen and A. Mandelbaum, Stochastic discrete flow networks: Diffusion approximations and bottlenecks, Ann. Probab. 19 (1991) 1436\u20131519.","journal-title":"Ann. Probab."},{"key":"313798_CR6","first-page":"49","volume":"5","author":"J.G. Dai","year":"1995","unstructured":"J.G. Dai, On the positive Harris recurrence for multiclass queueing networks: A unified approach via fluid limit models, Ann. Appl. Probab. 5 (1995) 49\u201377.","journal-title":"Ann. Appl. Probab."},{"key":"313798_CR7","first-page":"31","volume":"35","author":"P. Dupuis","year":"1991","unstructured":"P. Dupuis and H. Ishii, On Lipschitz continuity of the solution mapping to the Skorokhod problem with applications, Stochastics 35 (1991) 31\u201362.","journal-title":"Stochastics"},{"key":"313798_CR8","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/BF02073589","volume":"44","author":"P. Dupuis","year":"1993","unstructured":"P. Dupuis and A. Nagurney, Dynamical systems and variational inequalities, Ann. Oper. Res. 44 (1993) 9\u201342.","journal-title":"Ann. Oper. Res."},{"key":"313798_CR9","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1023\/A:1019186720196","volume":"28","author":"P. Dupuis","year":"1998","unstructured":"P. Dupuis and K. Ramanan, A Skorokhod problem formulation and large deviation analysis of a processor sharing model, Queueing Systems 28 (1998) 109\u2013124.","journal-title":"Queueing Systems"},{"key":"313798_CR10","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s004400050269","volume":"115","author":"P. Dupuis","year":"1999","unstructured":"P. Dupuis and K. Ramanan, Convex duality and the Skorokhod problem \u2013 I, Probab. Theory Related Fields 115 (1999) 153\u2013195.","journal-title":"Probab. Theory Related Fields"},{"key":"313798_CR11","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/s004400050270","volume":"115","author":"P. Dupuis","year":"1999","unstructured":"P. Dupuis and K. Ramanan, Convex duality and the Skorokhod problem \u2013 II, Probab. Theory Related Fields 115 (1999) 197\u2013236.","journal-title":"Probab. Theory Related Fields"},{"key":"313798_CR12","doi-asserted-by":"crossref","unstructured":"A. Elwalid and D. Mitra, Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes, in: Proc. of IEEE INFOCOM 99, 1999.","DOI":"10.1109\/INFCOM.1999.751679"},{"key":"313798_CR13","first-page":"302","volume":"9","author":"J.M. Harrison","year":"1981","unstructured":"J.M. Harrison and M.I. Reiman, Reflected Brownian motion on an orthant, Ann. Probab. 9 (1981) 302\u2013308.","journal-title":"Ann. Probab."},{"key":"313798_CR14","unstructured":"V.S. Kozyakin, A. Mandelbaum and A.A. Vladimirov, Absolute stability and dynamic complementarity, Preprint (1993)."},{"key":"313798_CR15","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1002\/cpa.3160370408","volume":"37","author":"P.-L. Lions","year":"1984","unstructured":"P.-L. Lions and A.-S. Sznitman, Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math. 37 (1984) 511\u2013553.","journal-title":"Comm. Pure Appl. Math."},{"key":"313798_CR16","doi-asserted-by":"crossref","first-page":"1406","DOI":"10.1109\/9.106156","volume":"36","author":"S.H. Lu","year":"1991","unstructured":"S.H. Lu and P.R. Kumar, Distributed scheduling based on due dates and buffer priorities, IEEE Trans. Automat. Control 36 (1991) 1406\u20131416.","journal-title":"IEEE Trans. Automat. Control"},{"key":"313798_CR17","volume-title":"Large deviations of feedforward queueing networks","author":"K. Majewski","year":"1996","unstructured":"K. Majewski, Large deviations of feedforward queueing networks, Ph.D. thesis, Ludwig-Maximilian-Universit\u00e4t M\u00fcnchen (1996)."},{"key":"313798_CR18","unstructured":"A. Mandelbaum, The dynamic complementarity problem, Unpublished manuscript (1989)."},{"key":"313798_CR19","unstructured":"A. Mandelbaum and L. Van der Heyden, A characterization of strictly semi-monotone matrices, Unpublished manuscript (1986)."},{"key":"313798_CR20","doi-asserted-by":"crossref","first-page":"946","DOI":"10.1214\/aoap\/1177004601","volume":"5","author":"S. Meyn","year":"1995","unstructured":"S. Meyn, Transience of multiclass queueing networks via fluid limit models, Ann. Appl. Probab. 5 (1995) 946\u2013957.","journal-title":"Ann. Appl. Probab."},{"key":"313798_CR21","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1287\/moor.16.1.90","volume":"16","author":"W. Peterson","year":"1991","unstructured":"W. Peterson, A heavy traffic limit theorem for networks of queues with multiple customer types, Math. Oper. Res. 16 (1991) 90\u2013118.","journal-title":"Math. Oper. Res."},{"key":"313798_CR22","first-page":"1070","volume":"8","author":"K. Ramanan","year":"1998","unstructured":"K. Ramanan and P. Dupuis, Large deviation analysis of data streams that share a buffer, Ann. Appl. Probab. 8 (1998) 1070\u20131129.","journal-title":"Ann. Appl. Probab."},{"key":"313798_CR23","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1287\/moor.9.3.441","volume":"9","author":"M.I. Reiman","year":"1984","unstructured":"M.I. Reiman, Open queueing networks in heavy traffic, Math. Oper. Res. 9 (1984) 441\u2013458.","journal-title":"Math. Oper. Res."},{"key":"313798_CR24","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/BF01848132","volume":"77","author":"M. Reiman","year":"1988","unstructured":"M. Reiman and R.J. Williams, A boundary property of semimartingale reflecting Brownian motions, Probab. Theory Related Fields 77 (1988) 87\u201397.","journal-title":"Probab. Theory Related Fields"},{"key":"313798_CR25","first-page":"3","volume":"28","author":"A.N. Rybko","year":"1992","unstructured":"A.N. Rybko and A.L. Stolyar, Ergodicity of stochastic processes describing the operation of open queueing networks, Problemy Peredachi Informatsii 28 (1992) 3\u201326.","journal-title":"Problemy Peredachi Informatsii"},{"key":"313798_CR26","first-page":"805","volume":"9","author":"J. Samuelson","year":"1958","unstructured":"J. Samuelson, R.M. Thrall and O. Wesler, A partition theorem for Euclidean N-space, Proc. Amer. Math. Soc. 9 (1958) 805\u2013807.","journal-title":"Proc. Amer. Math. Soc."},{"key":"313798_CR27","doi-asserted-by":"crossref","first-page":"1635","DOI":"10.1214\/aoms\/1177697379","volume":"40","author":"A.F. Veinnot Jr.","year":"1969","unstructured":"A.F. Veinnot, Jr., Discrete dynamic programming with sensitive discount optimaility criteria, Ann. Math. Statist. 40 (1969) 1635\u20131660.","journal-title":"Ann. Math. Statist."}],"container-title":["Queueing Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1011037419624.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1011037419624\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1011037419624.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T04:30:22Z","timestamp":1754454622000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1011037419624"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,12]]},"references-count":27,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2000,12]]}},"alternative-id":["313798"],"URL":"https:\/\/doi.org\/10.1023\/a:1011037419624","relation":{},"ISSN":["0257-0130","1572-9443"],"issn-type":[{"type":"print","value":"0257-0130"},{"type":"electronic","value":"1572-9443"}],"subject":[],"published":{"date-parts":[[2000,12]]}}}