{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T12:05:15Z","timestamp":1790424315783,"version":"4.1.0"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2019,5,25]],"date-time":"2019-05-25T00:00:00Z","timestamp":1558742400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,5,25]],"date-time":"2019-05-25T00:00:00Z","timestamp":1558742400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Queueing Syst"],"published-print":{"date-parts":[[2019,8]]},"DOI":"10.1007\/s11134-019-09617-y","type":"journal-article","created":{"date-parts":[[2019,5,25]],"date-time":"2019-05-25T02:32:01Z","timestamp":1558751521000},"page":"203-232","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A stochastic analysis of a network with two levels of service"],"prefix":"10.1007","volume":"92","author":[{"given":"Vianney","family":"B\u0153uf","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8122-8880","authenticated-orcid":false,"given":"Philippe","family":"Robert","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,5,25]]},"reference":[{"key":"9617_CR1","doi-asserted-by":"crossref","unstructured":"Allamigeon, X., B\u0153uf, V., Gaubert, S.: Performance evaluation of an emergency call center: tropical polynomial systems applied to timed Petri nets, FORMATS\u201915. Lecture Notes in Computer Science, vol. 9268. Springer (2015)","DOI":"10.1007\/978-3-319-22975-1_2"},{"key":"9617_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.peva.2017.04.007","volume":"113","author":"X Allamigeon","year":"2017","unstructured":"Allamigeon, X., B\u0153uf, V., Gaubert, S.: Stationary solutions of discrete and continuous Petri nets with priorities. Perform. Eval. 113, 1\u201312 (2017)","journal-title":"Perform. Eval."},{"key":"9617_CR3","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1017\/S0027763000017232","volume":"60","author":"RF Anderson","year":"1976","unstructured":"Anderson, R.F., Orey, S.: Small random perturbation of dynamical systems with reflecting boundary. Nagoya Math. J. 60, 189\u2013216 (1976)","journal-title":"Nagoya Math. J."},{"key":"9617_CR4","first-page":"233","volume-title":"Queueing Networks with Blocking: Analysis, Solution Algorithms and Properties","author":"S Balsamo","year":"2011","unstructured":"Balsamo, S.: Queueing Networks with Blocking: Analysis, Solution Algorithms and Properties, pp. 233\u2013257. Springer, Berlin (2011)"},{"key":"9617_CR5","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1007\/978-3-642-38143-0_5","volume-title":"Structure Theory of Petri Nets, Transactions on Petri Nets and Other Models of Concurrency VII","author":"E Best","year":"2013","unstructured":"Best, E., Wimmel, H.: Structure Theory of Petri Nets, Transactions on Petri Nets and Other Models of Concurrency VII, pp. 162\u2013224. Springer, Berlin (2013)"},{"issue":"8","key":"9617_CR6","doi-asserted-by":"publisher","first-page":"1434","DOI":"10.1109\/TAC.2003.815038","volume":"48","author":"S Bhulai","year":"2003","unstructured":"Bhulai, S., Koole, G.: A queueing model for call blending in call centers. IEEE Trans. Autom. Control 48(8), 1434\u20131438 (2003)","journal-title":"IEEE Trans. Autom. Control"},{"key":"9617_CR7","series-title":"Wiley Series in Probability and Statistics: Probability and Statistics","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316962","volume-title":"Convergence of Probability Measures","author":"P Billingsley","year":"1999","unstructured":"Billingsley, P.: Convergence of Probability Measures. Wiley Series in Probability and Statistics: Probability and Statistics. Wiley, New York (1999)"},{"issue":"2","key":"9617_CR8","doi-asserted-by":"publisher","first-page":"408","DOI":"10.1287\/moor.16.2.408","volume":"16","author":"H Chen","year":"1991","unstructured":"Chen, H., Mandelbaum, A.: Discrete flow networks: bottleneck analysis and fluid approximations. Math. Oper. Res. 16(2), 408\u2013446 (1991)","journal-title":"Math. Oper. Res."},{"key":"9617_CR9","unstructured":"Cohen, G., Gaubert, S., Quadrat, J.-P.: Asymptotic throughput of continuous timed Petri nets. In: 34th Conference on Decision and Control (New Orleans) (1995)"},{"key":"9617_CR10","doi-asserted-by":"crossref","unstructured":"Dong, J., Perry, O.: Queueing models for patient-flow dynamics in inpatient wards. Available at SSRN 3246641 (2018)","DOI":"10.2139\/ssrn.3246641"},{"key":"9617_CR11","unstructured":"El Karoui, N., Chaleyat-Maurel, M.: Temps locaux, vol. 52\u201353, ch.\u00a0Un probl\u00e8me de r\u00e9flexion et ses applications au tempslocal et aux \u00e9quations diff\u00e9rentielles stochastiques sur $${{\\mathbb{R}}}$$, pp.\u00a0117\u2013144, Soci\u00e9t\u00e9 Math\u00e9matique de France,1978, Expos\u00e9s du S\u00e9minaire J. Az\u00e9ma-M. Yor, Paris (1976\u20131977)"},{"issue":"2","key":"9617_CR12","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1214\/aop\/1176994471","volume":"9","author":"JM Harrison","year":"1981","unstructured":"Harrison, J.M., Reiman, M.I.: Reflected Brownian motion on an orthant. Ann. Probab. 9(2), 302\u2013308 (1981)","journal-title":"Ann. Probab."},{"key":"9617_CR13","series-title":"Wiley Series in Probability and Mathematical Statistics","volume-title":"Reversibility and Stochastic Networks","author":"FP Kelly","year":"1979","unstructured":"Kelly, F.P.: Reversibility and Stochastic Networks. Wiley Series in Probability and Mathematical Statistics. Wiley, Chichester (1979)"},{"key":"9617_CR14","doi-asserted-by":"publisher","first-page":"473","DOI":"10.2307\/1427309","volume":"18","author":"FP Kelly","year":"1986","unstructured":"Kelly, F.P.: Blocking probabilities in large circuit-switched networks. Adv. Appl. Probab. 18, 473\u2013505 (1986)","journal-title":"Adv. Appl. Probab."},{"key":"9617_CR15","volume-title":"Poisson Processes, Oxford studies in probability","author":"JFC Kingman","year":"1993","unstructured":"Kingman, J.F.C.: Poisson Processes, Oxford studies in probability. Oxford Science Publications, The Clarendon Press, Oxford University Press, New York (1993)"},{"issue":"1","key":"9617_CR16","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1023\/A:1020949626017","volume":"113","author":"G Koole","year":"2002","unstructured":"Koole, G., Mandelbaum, A.: Queueing models of call centers: an introduction. Ann. Oper. Res. 113(1), 41\u201359 (2002)","journal-title":"Ann. Oper. Res."},{"key":"9617_CR17","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1090\/S0002-9947-1975-0410986-7","volume":"213","author":"TM Liggett","year":"1975","unstructured":"Liggett, T.M.: Ergodic theorems for the asymmetric simple exclusion process. Trans. Am. Math. Soc. 213, 237\u2013261 (1975)","journal-title":"Trans. Am. Math. Soc."},{"key":"9617_CR18","series-title":"Grundlehrender mathematischen Wissenschaften","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8542-4","volume-title":"Interacting Particle Systems","author":"TM Liggett","year":"1985","unstructured":"Liggett, T.M.: Interacting Particle Systems. Grundlehrender mathematischen Wissenschaften. Springer, New York (1985)"},{"issue":"4","key":"9617_CR19","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1109\/5.24143","volume":"77","author":"T Murata","year":"1989","unstructured":"Murata, T.: Petri nets: properties, analysis and applications. Proc. IEEE 77(4), 541\u2013580 (1989)","journal-title":"Proc. IEEE"},{"issue":"1","key":"9617_CR20","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1287\/mnsc.2014.2019","volume":"61","author":"G Pang","year":"2015","unstructured":"Pang, G., Perry, O.: A logarithmic safety staffing rule for contact centers with call blending. Manag. Sci. 61(1), 73\u201391 (2015)","journal-title":"Manag. Sci."},{"key":"9617_CR21","volume-title":"Stochastic Networks and Queues, Stochastic Modelling and Applied Probability Series","author":"P Robert","year":"2003","unstructured":"Robert, P.: Stochastic Networks and Queues, Stochastic Modelling and Applied Probability Series, vol. 52. Springer, New York (2003)"},{"key":"9617_CR22","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1137\/1107002","volume":"7","author":"AV Skorokhod","year":"1962","unstructured":"Skorokhod, A.V.: Stochastic equations for diffusion processes in a bounded region. Theory Probab. Appl. 7, 3\u201323 (1962)","journal-title":"Theory Probab. Appl."},{"key":"9617_CR23","doi-asserted-by":"publisher","first-page":"53","DOI":"10.4099\/jjm1924.34.0_53","volume":"34","author":"S Watanabe","year":"1964","unstructured":"Watanabe, S.: On discontinuous additive functionals and L\u00e9vy measures of a Markov process. Jpn. J. Math. 34, 53\u201370 (1964)","journal-title":"Jpn. J. Math."},{"issue":"2","key":"9617_CR24","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1007\/s11134-011-9220-7","volume":"68","author":"R Yang","year":"2011","unstructured":"Yang, R., Bhulai, S., Van der Mei, R.: Optimal resource allocation for multiqueue systems with a shared server pool. Queueing Syst. 68(2), 133\u2013163 (2011)","journal-title":"Queueing Syst."}],"container-title":["Queueing Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11134-019-09617-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11134-019-09617-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11134-019-09617-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,2]],"date-time":"2020-06-02T05:52:48Z","timestamp":1591077168000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11134-019-09617-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,25]]},"references-count":24,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2019,8]]}},"alternative-id":["9617"],"URL":"https:\/\/doi.org\/10.1007\/s11134-019-09617-y","relation":{},"ISSN":["0257-0130","1572-9443"],"issn-type":[{"value":"0257-0130","type":"print"},{"value":"1572-9443","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,25]]},"assertion":[{"value":"22 December 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 May 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 May 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}