{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T15:25:16Z","timestamp":1763479516162,"version":"3.43.0"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[1999,7,1]],"date-time":"1999-07-01T00:00:00Z","timestamp":930787200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[1999,7,1]],"date-time":"1999-07-01T00:00:00Z","timestamp":930787200000},"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":[[1999,7]]},"DOI":"10.1023\/a:1019174601483","type":"journal-article","created":{"date-parts":[[2003,2,19]],"date-time":"2003-02-19T18:30:27Z","timestamp":1045679427000},"page":"359-392","source":"Crossref","is-referenced-by-count":21,"title":["Moderate deviations for queues in critical loading"],"prefix":"10.1007","volume":"31","author":[{"given":"Anatolii A.","family":"Puhalskii","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"329554_CR1","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/BF01158960","volume":"16","author":"J. Abate","year":"1994","unstructured":"J. Abate, G.L. Choudhury and W. Whitt, Waiting-time tail probabilities in queues with long-tail service-time distributions, Queueing Systems 16 (1994) 311\u2013338.","journal-title":"Queueing Systems"},{"key":"329554_CR2","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1287\/opre.43.5.885","volume":"43","author":"J. Abate","year":"1995","unstructured":"J. Abate, G.L. Choudhury and W. Whitt, Exponential approximations for tail probabilities in queues, I: Waiting times, and II: Sojourn time and workload, Oper. Res. 43 (1995) 885\u2013901 and 44 (1996) 758\u2013763.","journal-title":"Oper. Res."},{"key":"329554_CR3","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1007\/BF01225324","volume":"5","author":"V. Anantharam","year":"1989","unstructured":"V. Anantharam, How large delays build up in a GI\/G\/1 queue, Queueing Systems 5 (1989) 345\u2013367.","journal-title":"Queueing Systems"},{"key":"329554_CR4","doi-asserted-by":"publisher","first-page":"143","DOI":"10.2307\/1426737","volume":"14","author":"S. Asmussen","year":"1982","unstructured":"S. Asmussen, Conditioned limit theorems relating a random walk to its associate, with applications to risk reserve processes and the GI\/GI\/1 queue, Adv. in Appl. Probab. 14 (1982) 143\u2013170.","journal-title":"Adv. in Appl. Probab."},{"key":"329554_CR5","volume-title":"Convergence of Probability Measures","author":"P. Billingsley","year":"1968","unstructured":"P. Billingsley, Convergence of Probability Measures (Wiley, New York, 1968)."},{"key":"329554_CR6","volume-title":"Stochastic Processes in Queueing Theory","author":"A.A. Borovkov","year":"1972","unstructured":"A.A. Borovkov, Stochastic Processes in Queueing Theory (Nauka, Moscow, 1972) (in Russian, English translation: Springer, Berlin, 1976)."},{"key":"329554_CR7","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1007\/BF01158430","volume":"20","author":"C.-S. Chang","year":"1995","unstructured":"C.-S. Chang, Sample path large deviations and intree networks, Queueing Systems 20 (1995) 7\u201336.","journal-title":"Queueing Systems"},{"key":"329554_CR8","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/978-1-4612-4062-4_14","volume-title":"Stochastic Networks","author":"C.-S. Chang","year":"1996","unstructured":"C.-S. Chang, D.D. Yao and T. Zajic, Moderate deviations for queues with long-range dependent input, in: Stochastic Networks, Lecture Notes in Statistics, Vol. 117 (Springer, New York, 1996) pp. 275\u2013298."},{"key":"329554_CR9","volume-title":"Proc.Imperial College Workshop on Applied Stochastic Processes","author":"H. Chen","year":"1991","unstructured":"H. Chen and A. Mandelbaum, Leontief systems, RBV's and RBM's, in: Proc.Imperial College Workshop on Applied Stochastic Processes, eds. M.H.A. Davis and R.J. Elliot (Gordon and Breach, London, 1991)."},{"key":"329554_CR10","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1007\/BF01149260","volume":"13","author":"H. Chen","year":"1993","unstructured":"H. Chen and W. Whitt, Diffusion approximations for open queueing networks with service interruptions, Queueing Systems 13 (1993) 335\u2013359.","journal-title":"Queueing Systems"},{"key":"329554_CR11","unstructured":"A. Dembo and O. Zeitouni, Large Deviations, Techniques and Applications (Jones and Bartlett, 1993)."},{"key":"329554_CR12","volume-title":"Large Deviations","author":"J.D. Deuschel","year":"1989","unstructured":"J.D. Deuschel and D.W. Stroock, Large Deviations (Academic Press, New York, 1989)."},{"key":"329554_CR13","first-page":"301","volume":"7","author":"R.L. Dobrushin","year":"1995","unstructured":"R.L. Dobrushin and E.A. Pechersky, Large deviations for tandem queueing systems, J. Appl. Math. Stochastic Anal. 7 (1995) 301\u2013330.","journal-title":"J. Appl. Math. Stochastic Anal."},{"key":"329554_CR14","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1017\/S0305004100073709","volume":"118","author":"N.G. Duffield","year":"1995","unstructured":"N.G. Duffield and N. O'Connell, Large deviations and overflow probabilities for the general single server queue, with applications, Math. Proc. Cambridge Philos. Soc. 118 (1995) 363\u2013374.","journal-title":"Math. Proc. Cambridge Philos. Soc."},{"key":"329554_CR15","doi-asserted-by":"publisher","first-page":"2689","DOI":"10.2307\/2154753","volume":"347","author":"P. Dupuis","year":"1995","unstructured":"P. Dupuis and R.S. Ellis, The large deviation principle for a general class of queueing systems I, Trans. Amer. Math. Soc. 347 (1995) 2689\u20132751.","journal-title":"Trans. Amer. Math. Soc."},{"key":"329554_CR16","first-page":"31","volume":"35","author":"P. Dupuis","year":"1991","unstructured":"P. Dupuis and H. Ishii, On Lipshitz continuity of the solution mapping to the Skorokhod problem, with applications, Stochastics 35 (1991) 31\u201362.","journal-title":"Stochastics"},{"key":"329554_CR17","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1214\/aop\/1176990947","volume":"18","author":"P. Dupuis","year":"1990","unstructured":"P. Dupuis, H. Ishii and H.M. Soner, A viscosity solution approach to the asymptotic analysis of queueing systems, Ann. Probab. 18 (1990) 226\u2013255.","journal-title":"Ann. Probab."},{"key":"329554_CR18","doi-asserted-by":"crossref","unstructured":"P. Dupuis and K. Ramanan, Convex duality and the Skorokhod problem, preprint (1998).","DOI":"10.1007\/s004400050269"},{"key":"329554_CR19","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/BF01149173","volume":"22","author":"A. Ganesh","year":"1996","unstructured":"A. Ganesh and V. Anantharam, Stationary tail probabilities in exponential server tandems with renewal arrivals, Queueing Systems 22 (1996) 203\u2013247.","journal-title":"Queueing Systems"},{"key":"329554_CR20","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1007\/978-1-4757-2418-9_19","volume-title":"Stochastic Networks","author":"P.W. Glynn","year":"1995","unstructured":"P.W. Glynn, Large deviations for the infinite server queue in heavy traffic, Stochastic Networks, eds. F.P. Kelly and R.J. Williams, IMA Volumes in Mathematics and its Applications, Vol. 71 (Springer, New York, 1995) pp. 387\u2013393."},{"key":"329554_CR21","doi-asserted-by":"publisher","first-page":"131","DOI":"10.2307\/3214953","volume":"31A","author":"P.W. Glynn","year":"1994","unstructured":"P.W. Glynn and W. Whitt, Logarithmic asymptotics for steady-state tail probabilities in a singleserver queue, J. Appl. Probab. 31A (1994) 131\u2013156.","journal-title":"J. Appl. Probab."},{"key":"329554_CR22","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":"329554_CR23","doi-asserted-by":"publisher","first-page":"150","DOI":"10.2307\/1426324","volume":"2","author":"D.L. Iglehart","year":"1970","unstructured":"D.L. Iglehart and W. Whitt, Multiple channel queues in heavy traffic, I and II, Adv. in Appl. Probab. 2 (1970) 150\u2013177 and 355\u2013369.","journal-title":"Adv. in Appl. Probab."},{"key":"329554_CR24","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1070\/RM1994v049n02ABEH002204","volume":"49","author":"I.A. Ignatyuk","year":"1994","unstructured":"I.A. Ignatyuk, V. Malyshev and V.V. Scherbakov, Boundary effects in large deviation problems, Russian Math. Surveys 49 (1994) 41\u201399.","journal-title":"Russian Math. Surveys"},{"key":"329554_CR25","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1111\/j.2517-6161.1962.tb00465.x","volume":"24","author":"J.F.C. Kingman","year":"1962","unstructured":"J.F.C. Kingman, On queues in heavy traffic, J. Roy. Statist. Soc. B 24 (1962) 383\u2013392.","journal-title":"J. Roy. Statist. Soc. B"},{"key":"329554_CR26","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 function space D[0,1), J. Appl. Probab. 10 (1973) 109\u2013121.","journal-title":"J. Appl. Probab."},{"key":"329554_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01153524","volume":"14","author":"R. Liptser","year":"1993","unstructured":"R.Sh. Liptser, Large deviations for a simple closed queueing model, Queueing Systems 14 (1993) 1\u201331.","journal-title":"Queueing Systems"},{"key":"329554_CR28","volume-title":"Theory of Martingales","author":"R. Liptser","year":"1986","unstructured":"R.Sh. Liptser and A.N. Shiryaev, Theory of Martingales (Nauka, Moscow, 1986) (in Russian, English translation: Kluwer, Dordrecht, 1989)."},{"key":"329554_CR29","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1023\/A:1019147006084","volume":"28","author":"K. Majewski","year":"1998","unstructured":"K. Majewski, Heavy traffic approximations of large deviations of feedforward queueing networks, Queueing Systems 28 (1998) 125\u2013155.","journal-title":"Queueing Systems"},{"key":"329554_CR30","unstructured":"A. Mandelbaum, The dynamic complementarity problem, unpublished manuscript (1989)."},{"key":"329554_CR31","doi-asserted-by":"publisher","first-page":"753","DOI":"10.2307\/3215100","volume":"34","author":"N. O'Connell","year":"1997","unstructured":"N. O'Connell, Large deviations for departures from a shared buffer, J. Appl. Probab. 34 (1997) 753\u2013766.","journal-title":"J. Appl. Probab."},{"key":"329554_CR32","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1239\/jap\/1032192568","volume":"35","author":"N. O'Connell","year":"1998","unstructured":"N. O'Connell, Large deviations for queue lengths at a multi-buffered resource, J. Appl. Probab. 35 (1998) 240\u2013245.","journal-title":"J. Appl. Probab."},{"key":"329554_CR33","first-page":"199","volume":"3","author":"Y. Prohorov","year":"1963","unstructured":"Yu.V. Prohorov, Transient phenomena in queueing processes, Liet. Mat. Rink. 3 (1963) 199\u2013206 (in Russian).","journal-title":"Liet. Mat. Rink."},{"key":"329554_CR34","first-page":"198","volume-title":"New Trends in Probability and Statistics","author":"A. Puhalskii","year":"1991","unstructured":"A. Puhalskii, On functional principle of large deviations, in: New Trends in Probability and Statistics, Vol. 1, eds. V. Sazonov and T. Shervashidze (VSP\/Mokslas, Vilnius, 1991) pp. 198\u2013218."},{"key":"329554_CR35","first-page":"27","volume":"49","author":"A. Puhalskii","year":"1994","unstructured":"A. Puhalskii, Large deviations of semimartingales via convergence of the predictable characteristics, Stochastics 49 (1994) 27\u201385.","journal-title":"Stochastics"},{"key":"329554_CR36","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/BF01158574","volume":"21","author":"A. Puhalskii","year":"1995","unstructured":"A. Puhalskii, Large deviation analysis of the single server queue, Queueing Systems 21 (1995) 5\u201366; Erratum: Queueing Systems 23 (1996) 337.","journal-title":"Queueing Systems"},{"key":"329554_CR37","first-page":"141","volume":"61","author":"A. Puhalskii","year":"1997","unstructured":"A. Puhalskii, Large deviations of semimartingales: a maxingale problem approach, I. Limits as solutions to a maxingale problem, Stochastics 61 (1997) 141\u2013243.","journal-title":"Stochastics"},{"key":"329554_CR38","doi-asserted-by":"publisher","first-page":"362","DOI":"10.1214\/aoap\/1034625336","volume":"7","author":"A. Puhalskii","year":"1997","unstructured":"A. Puhalskii and W. Whitt, Functional large deviation principles for first passage time processes, Ann. Appl. Probab. 7 (1997) 362\u2013381.","journal-title":"Ann. Appl. Probab."},{"key":"329554_CR39","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1017\/S0269964800005349","volume":"12","author":"A. Puhalskii","year":"1998","unstructured":"A. Puhalskii and W. Whitt, Functional large deviation principles for waiting and departure processes, Probab. Engrg. Inform. Sci. 12 (1998) 479\u2013507.","journal-title":"Probab. Engrg. Inform. Sci."},{"key":"329554_CR40","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":"329554_CR41","doi-asserted-by":"publisher","first-page":"567","DOI":"10.2307\/1427839","volume":"27","author":"J.S. Sadowsky","year":"1995","unstructured":"J.S. Sadowsky, The probability of large queue lengths and waiting times in a heterogeneous multiserver queue, part II: Positive recurrence and logarithmic limits, Adv. in Appl. Probab. 27 (1995) 567\u2013583.","journal-title":"Adv. in Appl. Probab."},{"key":"329554_CR42","doi-asserted-by":"publisher","first-page":"532","DOI":"10.2307\/1427838","volume":"27","author":"J.S. Sadowsky","year":"1995","unstructured":"J.S. Sadowsky and W. Szpankowski, The probability of large queue lengths and waiting times in a heterogeneous multiserver queue, part I: Tight limits, Adv. in Appl. Probab. 27 (1995) 532\u2013566.","journal-title":"Adv. in Appl. Probab."},{"key":"329554_CR43","volume-title":"Large Deviations for Performance Analysis","author":"A. Shwartz","year":"1995","unstructured":"A. Shwartz and A. Weiss, Large Deviations for Performance Analysis (Chapman and Hall, London, 1995)."},{"key":"329554_CR44","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1137\/1101022","volume":"1","author":"A.V. Skorohod","year":"1956","unstructured":"A.V. Skorohod, Limit theorems for stochastic processes, Theory Probab. Appl. 1 (1956) 261\u2013290.","journal-title":"Theory Probab. Appl."},{"key":"329554_CR45","doi-asserted-by":"publisher","first-page":"168","DOI":"10.2307\/3214800","volume":"29","author":"P. Tsoucas","year":"1992","unstructured":"P. Tsoucas, Rare events in series of queues, J. Appl. Probab. 29 (1992) 168\u2013175.","journal-title":"J. Appl. Probab."},{"key":"329554_CR46","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970241","volume-title":"Large Deviations and Applications","author":"S.R.S. Varadhan","year":"1984","unstructured":"S.R.S. Varadhan, Large Deviations and Applications (SIAM, Philadelphia, PA, 1984)."},{"key":"329554_CR47","volume-title":"Limit Theorems on Large Deviations for Markov Random Processes","author":"A.D. Wentzell","year":"1986","unstructured":"A.D. Wentzell, Limit Theorems on Large Deviations for Markov Random Processes (Nauka, Moscow, 1986) (in Russian, English translation: Reidel, Dordrecht, 1989)."},{"key":"329554_CR48","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1287\/moor.5.1.67","volume":"1","author":"W. Whitt","year":"1980","unstructured":"W. Whitt, Some useful functions for functional limit theorems, Math. Oper. Res. 1 (1980) 67\u201385.","journal-title":"Math. Oper. Res."}],"container-title":["Queueing Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1019174601483.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1019174601483\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1019174601483.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T04:40:05Z","timestamp":1754455205000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1019174601483"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,7]]},"references-count":48,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[1999,7]]}},"alternative-id":["329554"],"URL":"https:\/\/doi.org\/10.1023\/a:1019174601483","relation":{},"ISSN":["0257-0130","1572-9443"],"issn-type":[{"type":"print","value":"0257-0130"},{"type":"electronic","value":"1572-9443"}],"subject":[],"published":{"date-parts":[[1999,7]]}}}