{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,13]],"date-time":"2024-07-13T04:36:20Z","timestamp":1720845380156},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Queueing Syst"],"published-print":{"date-parts":[[2011,1]]},"DOI":"10.1007\/s11134-010-9197-7","type":"journal-article","created":{"date-parts":[[2010,11,9]],"date-time":"2010-11-09T23:48:02Z","timestamp":1289346482000},"page":"1-32","source":"Crossref","is-referenced-by-count":28,"title":["Rare event asymptotics for a random walk in\u00a0the\u00a0quarter plane"],"prefix":"10.1007","volume":"67","author":[{"given":"Fabrice","family":"Guillemin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Johan S. H.","family":"van Leeuwaarden","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2010,11,11]]},"reference":[{"key":"9197_CR1","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/s11134-009-9140-y","volume":"62","author":"I.J.B.F. Adan","year":"2009","unstructured":"Adan, I.J.B.F., Foley, R.D., McDonald, D.R.: Exact asymptotics for the stationary distribution of a Markov chain: a production model. Queueing Syst. 62, 311\u2013344 (2009)","journal-title":"Queueing Syst."},{"key":"9197_CR2","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1070\/RM2001v056n05ABEH000398","volume":"56","author":"A.A. Borovkov","year":"2001","unstructured":"Borovkov, A.A., Mogul\u2019skii, A.A.: Large deviations for Markov chains in the positive quadrant. Russ. Math. Surv. 56, 803\u2013916 (2001)","journal-title":"Russ. Math. Surv."},{"key":"9197_CR3","first-page":"1003","volume-title":"Proceedings of ITC 17","author":"S.C. Borst","year":"2001","unstructured":"Borst, S.C., Boxma, O.J., van Uitert, M.J.G.: Two coupled queues with heterogeneous traffic. In: Proceedings of ITC 17, pp. 1003\u20131014. North-Holland, Amsterdam (2001)"},{"key":"9197_CR4","doi-asserted-by":"crossref","first-page":"1451","DOI":"10.1214\/105051605000000052","volume":"15","author":"M. Bousquet-M\u00e9lou","year":"2005","unstructured":"Bousquet-M\u00e9lou, M.: Walks in the quarter plane: Kreweras\u2019 algebraic model. Ann. Appl. Probab. 15, 1451\u20131491 (2005)","journal-title":"Ann. Appl. Probab."},{"key":"9197_CR5","volume-title":"Boundary Value Problems in Queueing System Analysis","author":"J.W. Cohen","year":"1983","unstructured":"Cohen, J.W., Boxma, O.J.: Boundary Value Problems in Queueing System Analysis. North-Holland, Amsterdam (1983)"},{"key":"9197_CR6","volume-title":"Asymptotic Methods in Analysis","author":"N.G. Bruijn De","year":"1981","unstructured":"De Bruijn, N.G.: Asymptotic Methods in Analysis. Dover, New York (1981)"},{"key":"9197_CR7","volume-title":"Multi-Access, Reservations and Queues","author":"D. Denteneer","year":"2008","unstructured":"Denteneer, D., van Leeuwaarden, J.S.H.: Multi-Access, Reservations and Queues. Springer, New York (2008)"},{"key":"9197_CR8","volume-title":"Calcul Infinit\u00e9simal","author":"J. Dieudonne","year":"1980","unstructured":"Dieudonne, J.: Calcul Infinit\u00e9simal. Hermann, Paris (1980)"},{"key":"9197_CR9","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1002\/(SICI)1098-2418(199701\/03)10:1\/2<103::AID-RSA5>3.0.CO;2-Z","volume":"10","author":"M. Drmota","year":"1997","unstructured":"Drmota, M.: Systems of functional equations. Random Struct. Algorithms 10, 103\u2013124 (1997)","journal-title":"Random Struct. Algorithms"},{"key":"9197_CR10","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/BF00535168","volume":"47","author":"G. Fayolle","year":"1979","unstructured":"Fayolle, G., Iasnogorodski, R.: Two coupled processors: The reduction to a Riemann\u2013Hilbert problem. Z. Wahrscheinlichkeitstheor. Verw. Geb. 47, 325\u2013351 (1979)","journal-title":"Z. Wahrscheinlichkeitstheor. Verw. Geb."},{"key":"9197_CR11","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-60001-2","volume-title":"Random Walks in the Quarter Plane","author":"G. Fayolle","year":"1999","unstructured":"Fayolle, G., Iasnogorodski, R., Malyshev, V.: Random Walks in the Quarter Plane. Springer, New York (1999)"},{"key":"9197_CR12","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511801655","volume-title":"Analytic Combinatorics","author":"P. Flajolet","year":"2009","unstructured":"Flajolet, P., Sedgewick, R.: Analytic Combinatorics. Cambridge University Press, Cambridge (2009)"},{"key":"9197_CR13","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1002\/(SICI)1098-2418(199710)11:3<223::AID-RSA2>3.0.CO;2-2","volume":"11","author":"P. Flajolet","year":"1988","unstructured":"Flajolet, P., Gourdon, X., Martinez, C.: Patterns in random binary search trees. Random Struct. Algorithms 11, 223\u2013244 (1988)","journal-title":"Random Struct. Algorithms"},{"key":"9197_CR14","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1017\/S0269964800001376","volume":"3","author":"L. Flatto","year":"1989","unstructured":"Flatto, L.: The longer queue model. Probab. Eng. Inf. Sci. 3, 537\u2013559 (1989)","journal-title":"Probab. Eng. Inf. Sci."},{"key":"9197_CR15","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1137\/0144074","volume":"44","author":"L. Flatto","year":"1984","unstructured":"Flatto, L., Hahn, S.: Two parallel queues created by arrivals with two demands. I. SIAM J. Appl. Math. 44, 1041\u20131053 (1984)","journal-title":"SIAM J. Appl. Math."},{"key":"9197_CR16","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1214\/aoap\/1015345342","volume":"11","author":"R.D. Foley","year":"2001","unstructured":"Foley, R.D., McDonald, D.R.: Join the shortest queue: Stability and exact asymptotics. Ann. Appl. Probab. 11, 569\u2013607 (2001)","journal-title":"Ann. Appl. Probab."},{"key":"9197_CR17","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1214\/105051604000000666","volume":"15","author":"R.D. Foley","year":"2005","unstructured":"Foley, R.D., McDonald, D.R.: Large deviations of a modified Jackson network: Stability and rough asymptotics. Ann. Appl. Probab. 15, 519\u2013541 (2005)","journal-title":"Ann. Appl. Probab."},{"key":"9197_CR18","doi-asserted-by":"crossref","first-page":"542","DOI":"10.1214\/105051604000000675","volume":"15","author":"R.D. Foley","year":"2005","unstructured":"Foley, R.D., McDonald, D.R.: Bridges and networks: exact asymptotics. Ann. Appl. Probab. 15, 542\u2013586 (2005)","journal-title":"Ann. Appl. Probab."},{"key":"9197_CR19","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1239\/jap\/1091543429","volume":"41","author":"F. Guillemin","year":"2004","unstructured":"Guillemin, F., Pinchon, D.: Analysis of generalized processor-sharing systems with two classes of customers and exponential services. J. Appl. Probab. 41, 832\u2013858 (2004)","journal-title":"J. Appl. Probab."},{"key":"9197_CR20","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1081\/STM-200046489","volume":"21","author":"L. Haque","year":"2005","unstructured":"Haque, L., Liu, L., Zhao, Y.Q.: Sufficient conditions for a geometric tail in a QBD process with countably many levels and phases. Stoch. Models 21, 77\u201399 (2005)","journal-title":"Stoch. Models"},{"key":"9197_CR21","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1070\/RM1994v049n02ABEH002204","volume":"49","author":"I.A. Ignatyuk","year":"1994","unstructured":"Ignatyuk, I.A., Malyshev, V.A., Scherbakov, V.V.: Boundary effects in a large deviation problem. Russ. Math. Surv. 49, 41\u201399 (1994)","journal-title":"Russ. Math. Surv."},{"key":"9197_CR22","doi-asserted-by":"crossref","first-page":"2057","DOI":"10.1214\/105051604000000477","volume":"14","author":"D.P. Kroese","year":"2004","unstructured":"Kroese, D.P., Scheinhardt, W.R.W., Taylor, P.G.: Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process. Ann. Appl. Probab. 14, 2057\u20132089 (2004)","journal-title":"Ann. Appl. Probab."},{"key":"9197_CR23","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1081\/STM-200056021","volume":"21","author":"H. Li","year":"2005","unstructured":"Li, H., Zhao, Y.Q.: A retrial queue with a constant retrial rate, server downs and impatient customers. Stoch. Models 21, 531\u2013550 (2005)","journal-title":"Stoch. Models"},{"key":"9197_CR24","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1287\/moor.1090.0375","volume":"34","author":"M. Miyazawa","year":"2009","unstructured":"Miyazawa, M.: Tail decay rates in double QBD processes and related reflected random walks. Math. Oper. Res. 34, 547\u2013575 (2009)","journal-title":"Math. Oper. Res."},{"key":"9197_CR25","doi-asserted-by":"crossref","first-page":"1231","DOI":"10.1239\/aap\/1103662965","volume":"36","author":"M. Miyazawa","year":"2004","unstructured":"Miyazawa, M., Zhao, Y.Q.: The stationary tail asymptotics in the GI\/G\/1-type queue with countably many background states. Adv. Appl. Probab. 36, 1231\u20131251 (2004)","journal-title":"Adv. Appl. Probab."},{"key":"9197_CR26","volume-title":"Matrix-Geometric Solutions in Stochastic Models, an Algorithmic Approach","author":"M.F. Neuts","year":"1981","unstructured":"Neuts, M.F.: Matrix-Geometric Solutions in Stochastic Models, an Algorithmic Approach. Johns Hopkins University Press, Baltimore (1981)"},{"key":"9197_CR27","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1137\/050643866","volume":"50","author":"R. Pemantle","year":"2008","unstructured":"Pemantle, R., Wilson, M.C.: Twenty combinatorial examples of asymptotics derived from multivariate generating functions. SIAM Rev. 50, 199\u2013272 (2008)","journal-title":"SIAM Rev."},{"key":"9197_CR28","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/S0167-6377(03)00046-4","volume":"31","author":"J.A.C. Resing","year":"2003","unstructured":"Resing, J.A.C., \u00d6rmeci, L.: A tandem queueing model with coupled processors. Oper. Res. Lett. 31, 383\u2013389 (2003)","journal-title":"Oper. Res. Lett."},{"key":"9197_CR29","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1239\/jap\/1110381381","volume":"42","author":"Y. Sakuma","year":"2005","unstructured":"Sakuma, Y., Miyazawa, M.: On the effect of finite buffer truncation in a two-node Jackson network. J. Appl. Probab. 42, 199\u2013222 (2005)","journal-title":"J. Appl. Probab."},{"key":"9197_CR30","volume-title":"Large Deviations for Performance Analysis, Queues, Communications and Computing","author":"A. Shwartz","year":"1995","unstructured":"Shwartz, A., Weiss, A.: Large Deviations for Performance Analysis, Queues, Communications and Computing. Chapman & Hall, London (1995)"},{"key":"9197_CR31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1081\/STM-100001397","volume":"17","author":"Y. Takahashi","year":"2001","unstructured":"Takahashi, Y., Fujimoto, K., Makimoto, N.: Geometric decay of the steady-state probabilities in a quasi-birth-and-death process with a countable number of phases. Stoch. Models 17, 1\u201324 (2001)","journal-title":"Stoch. Models"},{"key":"9197_CR32","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s11134-005-1683-y","volume":"51","author":"J.S.H. Leeuwaarden van","year":"2005","unstructured":"van Leeuwaarden, J.S.H., Resing, J.A.C.: A tandem queue with coupled processors: computational issues. Queueing Syst. 51, 29\u201352 (2005)","journal-title":"Queueing Syst."}],"container-title":["Queueing Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11134-010-9197-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,13]],"date-time":"2021-11-13T09:16:56Z","timestamp":1636795016000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11134-010-9197-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,11,11]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["9197"],"URL":"https:\/\/doi.org\/10.1007\/s11134-010-9197-7","relation":{},"ISSN":["0257-0130","1572-9443"],"issn-type":[{"value":"0257-0130","type":"print"},{"value":"1572-9443","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,11,11]]}}}