{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,15]],"date-time":"2025-08-15T00:35:41Z","timestamp":1755218141136,"version":"3.43.0"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1-4","license":[{"start":{"date-parts":[[2000,7,1]],"date-time":"2000-07-01T00:00:00Z","timestamp":962409600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2000,7,1]],"date-time":"2000-07-01T00:00:00Z","timestamp":962409600000},"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":[[2000,7]]},"DOI":"10.1023\/a:1019129708268","type":"journal-article","created":{"date-parts":[[2003,2,19]],"date-time":"2003-02-19T18:30:27Z","timestamp":1045679427000},"page":"23-54","source":"Crossref","is-referenced-by-count":8,"title":["A large closed queueing network with autonomous service and bottleneck"],"prefix":"10.1007","volume":"35","author":[{"given":"Vyacheslav M.","family":"Abramov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"329605_CR1","volume-title":"Investigation of a Queueing System with Service Depending on Queue-Length","author":"V.M. Abramov","year":"1991","unstructured":"V.M. Abramov, Investigation of a Queueing System with Service Depending on Queue-Length (Donish, Dushanbe, 1991) (in Russian)."},{"key":"329605_CR2","doi-asserted-by":"publisher","first-page":"606","DOI":"10.2307\/3215141","volume":"31","author":"V.M. Abramov","year":"1994","unstructured":"V.M. Abramov, On the asymptotic distribution of the maximum number of infectives in epidemic models with immigration, J. Appl. Probab. 31 (1994) 606\u2013613.","journal-title":"J. Appl. Probab."},{"key":"329605_CR3","unstructured":"V.M. Abramov, Queueing systems with autonomous service: up-and down-crossings approach, submitted for publication (1999)."},{"key":"329605_CR4","unstructured":"V.M. Abramov, Some results for large closed queueing networks with and without bottleneck: upand down-crossings approach, in preparation."},{"key":"329605_CR5","first-page":"413","volume":"35","author":"S.V. Anulova","year":"1990","unstructured":"S.V. Anulova and R.Sh. Liptser, Diffusion approximation for the processes with normal reflection, Theory Probab. Appl. 35 (1990) 413\u2013423.","journal-title":"Theory Probab. Appl."},{"key":"329605_CR6","volume-title":"Elements of the Theory of Markov Processes and their Applications","author":"A.T. Bharucha-Reid","year":"1960","unstructured":"A.T. Bharucha-Reid, Elements of the Theory of Markov Processes and their Applications (McGraw-Hill, New York, 1960)."},{"key":"329605_CR7","volume-title":"Convergence of Probability Measures","author":"P. Bilingsley","year":"1968","unstructured":"P. Bilingsley, Convergence of Probability Measures (Wiley, New York, 1968)."},{"key":"329605_CR8","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-9866-3","volume-title":"Stochastic Processes in Queueing Theory","author":"A.A. Borovkov","year":"1976","unstructured":"A.A. Borovkov, Stochastic Processes in Queueing Theory (Springer, Berlin, 1976)."},{"key":"329605_CR9","doi-asserted-by":"publisher","first-page":"408","DOI":"10.1287\/moor.16.2.408","volume":"16","author":"H. Chen","year":"1991","unstructured":"H. Chen and A. Mandelbaum, Discrete flow networks: Bottleneck analysis and fluid approximations, Math. Oper. Res. 16 (1991) 408\u2013446.","journal-title":"Math. Oper. Res."},{"key":"329605_CR10","first-page":"1463","volume":"19","author":"H. Chen","year":"1991","unstructured":"H. Chen and A. Mandelbaum, Discrete flow networks: Diffusion approximations and bottlenecks, Ann. Probab. 19 (1991) 1463\u20131519.","journal-title":"Ann. Probab."},{"key":"329605_CR11","doi-asserted-by":"publisher","first-page":"405","DOI":"10.2307\/3213014","volume":"14","author":"J.W. Cohen","year":"1977","unstructured":"J.W. Cohen, On up-and downcrossings, J. Appl. Probab. 14 (1977) 405\u2013410.","journal-title":"J. Appl. Probab."},{"key":"329605_CR12","volume-title":"Linear Estimation and Stochastic Control","author":"M.H.A. Davis","year":"1977","unstructured":"M.H.A. Davis, Linear Estimation and Stochastic Control (Chapman and Hall, London, 1977)."},{"key":"329605_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-59107-9","volume-title":"Capacit\u00b4es et Processus Stochastiques","author":"C. Dellacherie","year":"1972","unstructured":"C. Dellacherie, Capacit\u00b4es et Processus Stochastiques (Springer, Berlin, 1972)."},{"key":"329605_CR14","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02514-7","volume-title":"Limit Theorems for Stochastic Processes","author":"J. Jacod","year":"1987","unstructured":"J. Jacod and A.N. Shiryayev, Limit Theorems for Stochastic Processes (Springer, Berlin, 1987)."},{"key":"329605_CR15","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1016\/0167-6377(92)90009-R","volume":"11","author":"Y. Kogan","year":"1992","unstructured":"Y. Kogan, Another approach to asymptotic expansions for large closed queueing networks, Oper. Res. Lett. 11 (1992) 317\u2013321.","journal-title":"Oper. Res. Lett."},{"key":"329605_CR16","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/BF01153525","volume":"14","author":"Y. Kogan","year":"1993","unstructured":"Y. Kogan and R.Sh. Liptser, Limit non-stationary behavior of large closed queueing networks with bottlenecks, Queueing Systems 14 (1993) 33\u201355.","journal-title":"Queueing Systems"},{"key":"329605_CR17","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1214\/aoap\/1177004830","volume":"5","author":"Y. Kogan","year":"1995","unstructured":"Y. Kogan, R.Sh. Liptser and M. Shenfild, State-dependent Bene^s buffer model with fast loading and output rates, Ann. Appl. Probab. 5 (1995) 97\u2013120.","journal-title":"Ann. Appl. Probab."},{"key":"329605_CR18","first-page":"38","volume":"22","author":"Y. Kogan","year":"1986","unstructured":"Y. Kogan, R.Sh. Liptser and A.V. Smorodinskii, Gaussian diffusion approximation of closed Markov model of computer networks, Problems Inform. Transmission 22 (1986) 38\u201351.","journal-title":"Problems Inform. Transmission"},{"key":"329605_CR19","first-page":"3544","volume-title":"32nd IEEE CDC","author":"T. Konstantopoulos","year":"1993","unstructured":"T. Konstantopoulos, S.N. Papadakis and J. Walrand, Functional approximation theorems for controlled queueing networks, in: 32nd IEEE CDC, San Antonio, TX (1993) pp. 3544\u20133549."},{"key":"329605_CR20","doi-asserted-by":"publisher","first-page":"765","DOI":"10.2307\/3215154","volume":"31","author":"T. Konstantopoulos","year":"1994","unstructured":"T. Konstantopoulos, S.N. Papadakis and J. Walrand, Functional approximation theorems for controlled renewal processes, J. Appl. Probab. 31 (1994) 765\u2013776.","journal-title":"J. Appl. Probab."},{"key":"329605_CR21","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1137\/1133011","volume":"33","author":"E.V. Krichagina","year":"1988","unstructured":"E.V. Krichagina, R.Sh. Liptser and A.A. Puhalskii, Diffusion approximation for system with arrivals depending on queue, and with arbitrary service, Theory Probab. Appl. 33 (1988) 114\u2013124.","journal-title":"Theory Probab. Appl."},{"key":"329605_CR22","doi-asserted-by":"publisher","first-page":"109","DOI":"10.2307\/3212499","volume":"10","author":"T. Lindvall","year":"1973","unstructured":"T. Lindvall, Weak convergence of probability measures and random functions in the functional space D[0, \u221e], J. Appl. Probab. 10 (1973) 109\u2013121.","journal-title":"J. Appl. Probab."},{"key":"329605_CR23","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4293-0","volume-title":"Statistics of Random Processes","author":"R. Liptser","year":"1978","unstructured":"R.Sh. Liptser and A.N. Shiryayev, Statistics of Random Processes, Vols. I, II (Springer, Berlin, 1978)."},{"key":"329605_CR24","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-009-2438-3","volume-title":"Theory of Martingales","author":"R. Liptser","year":"1989","unstructured":"R.Sh. Liptser and A.N. Shiryayev, Theory of Martingales (Kluwer, Dordrecht, 1989)."},{"key":"329605_CR25","doi-asserted-by":"publisher","first-page":"569","DOI":"10.1214\/aoap\/1028903539","volume":"8","author":"A. Mandelbaum","year":"1998","unstructured":"A. Mandelbaum and G. Pats, State dependent stochastic networks. Part I. Approximations and applications with continuous diffusion limits, Ann. Appl. Probab. 8 (1998) 569\u2013646.","journal-title":"Ann. Appl. Probab."},{"key":"329605_CR26","volume-title":"Aufgaben und Lehrsatze aus der Analysis. Erster Band: Reihen, Integralrechnung, Functionentheorie","author":"G. Polya","year":"1964","unstructured":"G. Polya and G. Szego, Aufgaben und Lehrsatze aus der Analysis. Erster Band: Reihen, Integralrechnung, Functionentheorie (Springer, Berlin, 1964)."},{"key":"329605_CR27","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1137\/1106035","volume":"6","author":"A.V. Skorohod","year":"1961","unstructured":"A.V. Skorohod, Stochastic equations for diffusion processes in a bounded region, Theory Probab. Appl. 6 (1961) 264\u2013274.","journal-title":"Theory Probab. Appl."},{"key":"329605_CR28","doi-asserted-by":"publisher","first-page":"694","DOI":"10.2307\/2034973","volume":"14","author":"C. Stone","year":"1963","unstructured":"C. Stone, Weak convergence in stochastic processes defined on semi-infinite time intervals, Proc. Amer. Math. Soc. 14 (1963) 694\u2013696.","journal-title":"Proc. Amer. Math. Soc."},{"key":"329605_CR29","doi-asserted-by":"crossref","first-page":"163","DOI":"10.32917\/hmj\/1206135203","volume":"9","author":"H. Tanaka","year":"1979","unstructured":"H. Tanaka, Stochastic differential equations with reflected boundary condition in convex regions, Hiroshima Math. J. 9 (1979) 163\u2013177.","journal-title":"Hiroshima Math. J."},{"key":"329605_CR30","doi-asserted-by":"crossref","first-page":"1911","DOI":"10.1002\/j.1538-7305.1984.tb00084.x","volume":"63","author":"W. Whitt","year":"1984","unstructured":"W. Whitt, Open and closed models for networks of queues, AT & T Bell. Lab. Tech. J. 63 (1984) 1911\u20131979.","journal-title":"AT & T Bell. Lab. Tech. J."}],"container-title":["Queueing Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1019129708268.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1019129708268\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1019129708268.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T04:28:10Z","timestamp":1754454490000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1019129708268"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,7]]},"references-count":30,"journal-issue":{"issue":"1-4","published-print":{"date-parts":[[2000,7]]}},"alternative-id":["329605"],"URL":"https:\/\/doi.org\/10.1023\/a:1019129708268","relation":{},"ISSN":["0257-0130","1572-9443"],"issn-type":[{"type":"print","value":"0257-0130"},{"type":"electronic","value":"1572-9443"}],"subject":[],"published":{"date-parts":[[2000,7]]}}}