{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T03:55:04Z","timestamp":1776830104317,"version":"3.51.2"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2003,6,1]],"date-time":"2003-06-01T00:00:00Z","timestamp":1054425600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2003,6,1]],"date-time":"2003-06-01T00:00:00Z","timestamp":1054425600000},"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":[[2003,6]]},"DOI":"10.1023\/a:1024403704190","type":"journal-article","created":{"date-parts":[[2003,9,15]],"date-time":"2003-09-15T13:22:37Z","timestamp":1063632157000},"page":"109-123","source":"Crossref","is-referenced-by-count":101,"title":["Properties of the Reflected Ornstein\u2013Uhlenbeck Process"],"prefix":"10.1007","volume":"44","author":[{"given":"Amy R.","family":"Ward","sequence":"first","affiliation":[]},{"given":"Peter W.","family":"Glynn","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"5124094_CR1","doi-asserted-by":"crossref","first-page":"560","DOI":"10.2307\/1427408","volume":"19","author":"J. Abate","year":"1987","unstructured":"J. Abate and W. Whitt, Transient behavior of regulated Brownian motion, I: Starting at the origin, Adv. in Appl. Probab. 19 (1987) 560\u2013598.","journal-title":"Adv. in Appl. Probab."},{"key":"5124094_CR2","doi-asserted-by":"crossref","first-page":"599","DOI":"10.2307\/1427409","volume":"19","author":"J. Abate","year":"1987","unstructured":"J. Abate and W. Whitt, Transient behavior of regulated Brownian motion, II: Non-zero initial conditions, Adv. in Appl. Probab. 19 (1987) 599\u2013631.","journal-title":"Adv. in Appl. Probab."},{"issue":"2","key":"5124094_CR3","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1023\/A:1009970005784","volume":"1","author":"S. Asmussen","year":"1998","unstructured":"S. Asmussen, Extreme value theory for queues via cycle maxima, Extremes 1(2) (1998) 137\u2013168.","journal-title":"Extremes"},{"key":"5124094_CR4","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1017\/S0269964800003934","volume":"9","author":"A. Berger","year":"1995","unstructured":"A. Berger and W. Whitt, Maximum values in queueing processes, Probab. Engrg. Inform. Sci. 9 (1995) 375\u2013409.","journal-title":"Probab. Engrg. Inform. Sci."},{"key":"5124094_CR5","volume-title":"Asymptotic Methods in Queueing Theory","author":"A. Borovkov","year":"1984","unstructured":"A. Borovkov, Asymptotic Methods in Queueing Theory (Wiley, New York, 1984)."},{"key":"5124094_CR6","first-page":"463","volume-title":"Advances in Queueing: Theory, Methods, and Open Problems","author":"S. Browne","year":"1995","unstructured":"S. Browne and W. Whitt, Piecewise-linear diffusion processes, in: Advances in Queueing: Theory, Methods, and Open Problems, ed. J. Dshalalow (CRC Press, Boca Raton, FL, 1995) pp. 463\u2013480."},{"key":"5124094_CR7","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/0166-5316(94)90053-1","volume":"19","author":"E. Coffman","year":"1994","unstructured":"E. Coffman, A. Puhalskii, M. Reiman and P. Wright, Processor-shared buffers with reneging, Performance Evaluation 19 (1994) 25\u201346.","journal-title":"Processor-shared buffers with reneging, Performance Evaluation"},{"key":"5124094_CR8","doi-asserted-by":"crossref","first-page":"1096","DOI":"10.1287\/mnsc.41.6.1096","volume":"41","author":"P. Glynn","year":"1995","unstructured":"P.W. Glynn and D. Iglehart, Trading securities using trailing stops, Managm. Sci. 41 (1995) 1096\u2013 1106.","journal-title":"Managm. Sci."},{"key":"5124094_CR9","volume-title":"Brownian Motion and Stochastic Flow Systems","author":"J. Harrison","year":"1985","unstructured":"J.M. Harrison, Brownian Motion and Stochastic Flow Systems (Wiley, New York, 1985)."},{"key":"5124094_CR10","volume-title":"Brownian Motion and Stochastic Calculus","author":"I. Karatzas","year":"1991","unstructured":"I. Karatzas and S.E. Shreve, Brownian Motion and Stochastic Calculus (Springer, New York, 1991)."},{"key":"5124094_CR11","volume-title":"A Second Course in Stochastic Processes","author":"S. Karlin","year":"1976","unstructured":"S. Karlin and H. Taylor, A Second Course in Stochastic Processes (Academic Press, New York, 1976)."},{"key":"5124094_CR12","doi-asserted-by":"crossref","first-page":"866","DOI":"10.1214\/aoms\/1177699368","volume":"37","author":"J. Keilson","year":"1966","unstructured":"J. Keilson, A limit theorem for passage times in ergodic regenerative processes, Ann. Math. Statist. 37 (1966) 866\u2013870.","journal-title":"Ann. Math. Statist."},{"key":"5124094_CR13","doi-asserted-by":"crossref","first-page":"82","DOI":"10.2307\/3213722","volume":"20","author":"T. Lindvall","year":"1983","unstructured":"T. Lindvall, On coupling of diffusion processes, J. Appl. Probab. 20 (1983) 82\u201393.","journal-title":"J. Appl. Probab."},{"key":"5124094_CR14","volume-title":"Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics","author":"T. Lindvall","year":"1992","unstructured":"T. Lindvall, Lectures on the coupling method, in: Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics (Wiley, New York, 1992)."},{"key":"5124094_CR15","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1002\/cpa.3160370408","volume":"37","author":"P. Lions","year":"1984","unstructured":"P. Lions and A. Sznitman, Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math. 37 (1984) 511\u2013537.","journal-title":"Comm. Pure Appl. Math."},{"key":"5124094_CR16","doi-asserted-by":"crossref","first-page":"371","DOI":"10.2307\/1427395","volume":"20","author":"H. Rootzen","year":"1989","unstructured":"H. Rootzen, Maxima and exceedances of stationary Markov chains, Adv. in Appl. Probab. 20 (1989) 371\u2013390.","journal-title":"Adv. in Appl. Probab."},{"key":"5124094_CR17","volume-title":"Stochastic Processes","author":"S. Ross","year":"1996","unstructured":"S. Ross, Stochastic Processes (Wiley, New York, 1996)."},{"key":"5124094_CR18","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/0304-4149(87)90043-3","volume":"27","author":"R. Serfozo","year":"1988","unstructured":"R. Serfozo, Extreme values of birth and death processes and queues, Stochastic Process. Appl. 27 (1988) 291\u2013306.","journal-title":"Stochastic Process. Appl."},{"key":"5124094_CR19","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1145\/229493.229496","volume":"6","author":"R. Srikant","year":"1996","unstructured":"R. Srikant and W. Whitt, Simulation run lengths to estimate blocking probabilities, ACMTrans.Modeling Comput. Simulation 6 (1996) 7\u201352.","journal-title":"ACMTrans.Modeling Comput. Simulation"},{"key":"5124094_CR20","unstructured":"A. Ward and P. Glynn, A diffusion approximation for a GI\/G\/1 queue with reneging, Working paper (2002)."},{"key":"5124094_CR21","unstructured":"A. Ward and P. Glynn, A diffusion approximation for a Markovian queue with reneging, under review (2002)."}],"container-title":["Queueing Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1024403704190.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1024403704190\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1024403704190.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T04:26:07Z","timestamp":1754454367000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1024403704190"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,6]]},"references-count":21,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2003,6]]}},"alternative-id":["5124094"],"URL":"https:\/\/doi.org\/10.1023\/a:1024403704190","relation":{},"ISSN":["0257-0130","1572-9443"],"issn-type":[{"value":"0257-0130","type":"print"},{"value":"1572-9443","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,6]]}}}