{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T16:43:30Z","timestamp":1760978610431,"version":"3.43.0"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[1998,11,1]],"date-time":"1998-11-01T00:00:00Z","timestamp":909878400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[1998,11,1]],"date-time":"1998-11-01T00:00:00Z","timestamp":909878400000},"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":[[1998,11]]},"DOI":"10.1023\/a:1019156702875","type":"journal-article","created":{"date-parts":[[2003,2,19]],"date-time":"2003-02-19T18:30:27Z","timestamp":1045679427000},"page":"5-25","source":"Crossref","is-referenced-by-count":77,"title":["An invariance principle for semimartingale reflecting Brownian motions in an orthant"],"prefix":"10.1007","volume":"30","author":[{"given":"R.J.","family":"Williams","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"329521_CR1","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1080\/17442509108833680","volume":"34","author":"A. Bernard","year":"1991","unstructured":"A. Bernard and A. El Kharroubi, R\u00e9gulation de processus dans le premier orthant de Rn, Stochastics and Stochastics Rep. 34 (1991) 149-167.","journal-title":"Stochastics and Stochastics Rep"},{"key":"329521_CR2","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1023\/A:1019160803783","volume":"30","author":"M. Bramson","year":"1998","unstructured":"M. Bramson, State space collapse with application to heavy traffic limits for multiclass queueing networks, Queueing Systems 30 (1998) 89-148.","journal-title":"Queueing Systems"},{"key":"329521_CR3","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/BF01206556","volume":"23","author":"H. Chen","year":"1996","unstructured":"H. Chen and H. Zhang, Diffusion approximations for re-entrant lines with a first-buffer-first-served priority discipline, Queueing Systems 23 (1996) 177-195.","journal-title":"Queueing Systems"},{"key":"329521_CR4","unstructured":"J.G. Dai and W. Dai, A heavy traffic limit theorem for a class of open queueing networks with finite buffers, submitted to Queueing Systems (1997)."},{"key":"329521_CR5","first-page":"26","volume":"4","author":"J.G. Dai","year":"1994","unstructured":"J.G. Dai and V. Nguyen, On the convergence of multiclass queueing networks in heavy traffic, Ann. Appl. Probab. 4 (1994) 26-42.","journal-title":"Ann. Appl. Probab."},{"key":"329521_CR6","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/BF01158928","volume":"13","author":"J.G. Dai","year":"1993","unstructured":"J.G. Dai and Y. Wang, Nonexistence of Brownian models of certain multiclass queueing networks, Queueing Systems 13 (1993) 41-46.","journal-title":"Queueing Systems"},{"key":"329521_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/1140001","volume":"40","author":"J.G. Dai","year":"1995","unstructured":"J.G. Dai and R.J. Williams, Existence and uniqueness of semimartingale reflecting Brownian motions in convex polyhedrons, Theory Probab. Appl. 40 (1995) 1-40.","journal-title":"Theory Probab. Appl."},{"key":"329521_CR8","volume-title":"Brownian approximations for queueing networks with finite buffers: Modeling, heavy traffic analysis and numerical implementations","author":"W. Dai","year":"1996","unstructured":"W. Dai, Brownian approximations for queueing networks with finite buffers: Modeling, heavy traffic analysis and numerical implementations, Ph.D. dissertation, School of Mathematics, Georgia Institute of Technology, Atlanta, GA (1996)."},{"key":"329521_CR9","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1080\/17442509108833688","volume":"35","author":"P. Dupuis","year":"1991","unstructured":"P. Dupuis and H. Ishii, On the Lipschitz continuity of the solution mapping to the Skorokhod problem, Stochastics and Stochastics Rep. 35 (1991) 31-62.","journal-title":"Stochastics and Stochastics Rep"},{"key":"329521_CR10","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316658","volume-title":"Markov Processes: Characterization and Convergence","author":"S.N. Ethier","year":"1986","unstructured":"S.N. Ethier and T.G. Kurtz, Markov Processes: Characterization and Convergence (Wiley, New York, 1986)."},{"key":"329521_CR11","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1093\/oso\/9780198523994.003.0004","volume-title":"Stochastic Networks: Theory and Applications","author":"J.M. Harrison","year":"1996","unstructured":"J.M. Harrison, The BIGSTEP approach to flow management in stochastic processing networks, in: Stochastic Networks: Theory and Applications, eds. F.P. Kelly, S. Zachary and I. Ziedins (Oxford Univ. Press, Oxford, 1996) pp. 57-90."},{"key":"329521_CR12","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) 302-308.","journal-title":"Ann. Probab."},{"key":"329521_CR13","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1007\/BF01225319","volume":"5","author":"J.M. Harrison","year":"1989","unstructured":"J.M. Harrison and L.M. Wein, Scheduling networks of queues: Heavy traffic analysis of a simple open network, Queueing Systems 5 (1989) 265-280.","journal-title":"Queueing Systems"},{"key":"329521_CR14","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/BF01158929","volume":"13","author":"F.P. Kelly","year":"1993","unstructured":"F.P. Kelly and C.N. Laws, Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling, Queueing Systems 13 (1993) 47-86.","journal-title":"Queueing Systems"},{"key":"329521_CR15","volume-title":"Diffusion approximations for optimal filtering of jump processes and for queueing networks","author":"D.P. Johnson","year":"1983","unstructured":"D.P. Johnson, Diffusion approximations for optimal filtering of jump processes and for queueing networks, Ph.D. dissertation, Department of Mathematics, University of Wisconsin, Madison, WI (1983)."},{"key":"329521_CR16","unstructured":"A. Mandelbaum and L. Van der Heyden, Complementarity and reflection (1987, unpublished work)."},{"key":"329521_CR17","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1287\/moor.16.1.90","volume":"9","author":"W.P. Peterson","year":"1991","unstructured":"W.P. Peterson, Diffusion approximations for networks of queues with multiple customer types, Math. Oper. Res. 9 (1991) 90-118.","journal-title":"Math. Oper. Res."},{"key":"329521_CR18","doi-asserted-by":"publisher","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) 441-458.","journal-title":"Math. Oper. Res."},{"key":"329521_CR19","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1007\/BF01848132","volume":"77","author":"M.I. Reiman","year":"1988","unstructured":"M.I. Reiman and R.J. Williams, A boundary property of semimartingale reflecting Brownian motions, Probab. Theory Related Fields 77 (1988) 87-97, and 80 (1989) 633.","journal-title":"Probab. Theory Related Fields"},{"key":"329521_CR20","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1137\/1101022","volume":"1","author":"A.V. Skorokhod","year":"1956","unstructured":"A.V. Skorokhod, Limit theorems for stochastic processes, Theory Probab. Appl. 1 (1956) 261-290.","journal-title":"Theory Probab. Appl."},{"key":"329521_CR21","volume-title":"Multidimensional Diffusion Processes","author":"D.W. Stroock","year":"1979","unstructured":"D.W. Stroock and S.R.S. Varadhan, Multidimensional Diffusion Processes (Springer, New York, 1979)."},{"key":"329521_CR22","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1002\/cpa.3160240206","volume":"24","author":"D.W. Stroock","year":"1971","unstructured":"D.W. Stroock and S.R.S. Varadhan, Diffusion processes with boundary conditions, Comm. Pure Appl. Math. 24 (1971) 147-225.","journal-title":"Comm. Pure Appl. Math."},{"key":"329521_CR23","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/BF01292674","volume":"96","author":"L.M. Taylor","year":"1993","unstructured":"L.M. Taylor and R.J. Williams, Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant, Probab. Theory Related Fields 96 (1993) 283-317.","journal-title":"Probab. Theory Related Fields"},{"key":"329521_CR24","doi-asserted-by":"crossref","first-page":"1020","DOI":"10.1287\/mnsc.39.8.1020","volume":"39","author":"W. Whitt","year":"1993","unstructured":"W. Whitt, Large fluctuations in a deterministic multiclass network of queues, Managm. Sci. 39 (1993) 1020-1028.","journal-title":"Managm. Sci."},{"key":"329521_CR25","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1093\/oso\/9780198523994.003.0003","volume-title":"Stochastic Networks: Theory and Applications","author":"R.J. Williams","year":"1996","unstructured":"R.J. Williams, On the approximation of queueing networks in heavy traffic, in: Stochastic Networks: Theory and Applications, eds. F.P. Kelly, S. Zachary and I. Ziedins (Oxford Univ. Press, Oxford, 1996) pp. 35-56."},{"key":"329521_CR26","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1023\/A:1019108819713","volume":"30","author":"R.J. Williams","year":"1998","unstructured":"R.J. Williams, Diffusion approximations for open multiclass queueing networks: sufficient conditions involving state space collapse, Queueing Systems 30 (1998) 27-88.","journal-title":"Queueing Systems"}],"container-title":["Queueing Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1019156702875.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1019156702875\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1019156702875.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,5]],"date-time":"2025-08-05T13:07:17Z","timestamp":1754399237000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1019156702875"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,11]]},"references-count":26,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[1998,11]]}},"alternative-id":["329521"],"URL":"https:\/\/doi.org\/10.1023\/a:1019156702875","relation":{},"ISSN":["0257-0130","1572-9443"],"issn-type":[{"type":"print","value":"0257-0130"},{"type":"electronic","value":"1572-9443"}],"subject":[],"published":{"date-parts":[[1998,11]]}}}