{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T09:21:50Z","timestamp":1743067310099,"version":"3.40.3"},"publisher-location":"Cham","reference-count":30,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319464329"},{"type":"electronic","value":"9783319464336"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-46433-6_4","type":"book-chapter","created":{"date-parts":[[2016,9,15]],"date-time":"2016-09-15T07:19:35Z","timestamp":1473923975000},"page":"48-62","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Finding Steady States of Communicating Markov Processes Combining Aggregation\/Disaggregation with Tensor Techniques"],"prefix":"10.1007","author":[{"given":"Francisco","family":"Macedo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,9,16]]},"reference":[{"issue":"8","key":"4_CR1","doi-asserted-by":"publisher","first-page":"1947","DOI":"10.1007\/s11538-010-9517-4","volume":"72","author":"DF Anderson","year":"2010","unstructured":"Anderson, D.F., Craciun, G., Kurtz, T.G.: Product-form stationary distributions for deficiency zero chemical reaction networks. Bull. Math. Biol. 72(8), 1947\u20131970 (2010)","journal-title":"Bull. Math. Biol."},{"issue":"4","key":"4_CR2","doi-asserted-by":"publisher","first-page":"2007","DOI":"10.1214\/105051606000000466","volume":"16","author":"N Antunes","year":"2006","unstructured":"Antunes, N., Fricker, C., Robert, P., Tibi, D.: Analysis of loss networks with routing. Ann. Appl. Probab. 16(4), 2007\u20132026 (2006)","journal-title":"Ann. Appl. Probab."},{"key":"4_CR3","unstructured":"Bolten, M., Kahl, K., Kressner, D., Macedo, F., Sokolovi\u0107, S.: Multigrid methods combined with amen for tensor structured Markov chains with low rank approximation (2016). arXiv preprint \n                      arXiv:1605.06246"},{"key":"4_CR4","unstructured":"Bolten, M., Kahl, K., Sokolovi\u0107, S.: Multigrid methods for tensor structured Markov chains with low rank approximation (2014). arXiv preprint \n                      arXiv:1412.0937"},{"issue":"9","key":"4_CR5","doi-asserted-by":"publisher","first-page":"797","DOI":"10.1016\/j.peva.2009.12.005","volume":"67","author":"P Buchholz","year":"2010","unstructured":"Buchholz, P.: Product form approximations for communicating Markov processes. Perform. Eval. 67(9), 797\u2013815 (2010)","journal-title":"Perform. Eval."},{"issue":"3","key":"4_CR6","doi-asserted-by":"publisher","first-page":"1025","DOI":"10.1137\/060651161","volume":"29","author":"P Buchholz","year":"2007","unstructured":"Buchholz, P., Dayar, T.: On the convergence of a class of multilevel methods for large sparse Markov chains. SIAM J. Matrix Anal. Appl. 29(3), 1025\u20131049 (2007)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"4_CR7","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1007\/BF01396747","volume":"51","author":"R Chan","year":"1987","unstructured":"Chan, R.: Iterative methods for overflow queueing networks I. Numer. Math. 51, 143\u2013180 (1987)","journal-title":"Numer. Math."},{"key":"4_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-4190-8","volume-title":"Analyzing Markov Chains using Kronecker Products: Theory and Applications","author":"T Dayar","year":"2012","unstructured":"Dayar, T.: Analyzing Markov Chains using Kronecker Products: Theory and Applications. Springer Science & Business Media, Heidelberg (2012)"},{"issue":"6","key":"4_CR9","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1016\/S0020-0190(03)00343-0","volume":"87","author":"S Derisavi","year":"2003","unstructured":"Derisavi, S., Hermanns, H., Sanders, W.H.: Optimal state-space lumping in Markov chains. Inf. Process. Lett. 87(6), 309\u2013315 (2003)","journal-title":"Inf. Process. Lett."},{"key":"4_CR10","unstructured":"Dolgov, S.V., Savostyanov, D.V.: Alternating minimal energy methods for linear systems in higher dimensions. Part I: SPD systems. ArXiv e-prints, January 2013"},{"key":"4_CR11","unstructured":"Dolgov, S.V., Savostyanov, D.V.: Alternating minimal energy methods for linear systems in higher dimensions. Part II: Faster algorithm and application to nonsymmetric systems. ArXiv e-prints, April 2013"},{"key":"4_CR12","volume-title":"Matrix Computations","author":"GH Golub","year":"1996","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix Computations. Johns Hopkins University Press, Baltimore (1996)"},{"key":"4_CR13","volume-title":"Multi-Grid Methods and Applications","author":"W Hackbusch","year":"2003","unstructured":"Hackbusch, W.: Multi-Grid Methods and Applications. Springer, Heidelberg (2003)"},{"key":"4_CR14","doi-asserted-by":"crossref","unstructured":"Hillston, J., Marin, A., Rossi, S., Piazza, C.: Contextual lumpability. In: Proceedings of the 7th International Conference on Performance Evaluation Methodologies and Tools, pp. 194\u2013203. ICST (Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering) (2013)","DOI":"10.4108\/icst.valuetools.2013.254408"},{"key":"4_CR15","doi-asserted-by":"crossref","unstructured":"Horton, G., Leutenegger, S.T.: A multi-level solution algorithm for steady-state Markov chains. In: Gaither, B.D. (ed.), Proceedings of the ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, pp. 191\u2013200 (1994)","DOI":"10.1145\/183019.183040"},{"key":"4_CR16","doi-asserted-by":"publisher","first-page":"525","DOI":"10.1137\/0904037","volume":"4","author":"L Kaufman","year":"1983","unstructured":"Kaufman, L.: Matrix methods for queuing problems. SIAM J. Sci. Statist. Comput. 4, 525\u2013552 (1983)","journal-title":"SIAM J. Sci. Statist. Comput."},{"issue":"3","key":"4_CR17","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1137\/07070111X","volume":"51","author":"TG Kolda","year":"2009","unstructured":"Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Rev. 51(3), 455\u2013500 (2009)","journal-title":"SIAM Rev."},{"key":"4_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/978-3-319-10696-0_4","volume-title":"Quantitative Evaluation of Systems","author":"D Kressner","year":"2014","unstructured":"Kressner, D., Macedo, F.: Low-rank tensor methods for communicating Markov processes. In: Norman, G., Sanders, W. (eds.) QEST 2014. LNCS, vol. 8657, pp. 25\u201340. Springer, Heidelberg (2014)"},{"issue":"2","key":"4_CR19","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1016\/j.cam.2003.10.010","volume":"167","author":"AN Langville","year":"2004","unstructured":"Langville, A.N., Stewart, W.J.: The Kronecker product and stochastic automata networks. J. Comput. Appl. Math. 167(2), 429\u2013447 (2004)","journal-title":"J. Comput. Appl. Math."},{"issue":"22","key":"4_CR20","doi-asserted-by":"publisher","first-page":"9224","DOI":"10.1073\/pnas.0610987104","volume":"104","author":"E Levine","year":"2007","unstructured":"Levine, E., Hwa, T.: Stochastic fluctuations in metabolic pathways. Proc. Natl. Acad. Sci. U.S.A. 104(22), 9224\u20139229 (2007)","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"4_CR21","unstructured":"Macedo, F.: Benchmark problems on stochastic automata networks in tensor train format. Technical report, MATHICSE, EPF Lausanne, Switzerland (2015)"},{"key":"4_CR22","unstructured":"Oseledets, I.V.: MATLAB TT-Toolbox Version 2.2 (2011). \n                      http:\/\/spring.inm.ras.ru\/osel\/?page id=24"},{"issue":"5","key":"4_CR23","doi-asserted-by":"publisher","first-page":"2295","DOI":"10.1137\/090752286","volume":"33","author":"IV Oseledets","year":"2011","unstructured":"Oseledets, I.V.: Tensor-Train decomposition. SIAM J. Sci. Comput. 33(5), 2295\u20132317 (2011)","journal-title":"SIAM J. Sci. Comput."},{"issue":"5","key":"4_CR24","doi-asserted-by":"publisher","first-page":"3744","DOI":"10.1137\/090748330","volume":"31","author":"IV Oseledets","year":"2009","unstructured":"Oseledets, I.V., Tyrtyshnikov, E.E.: Breaking the curse of dimensionality, or how to use SVD in many dimensions. SIAM J. Sci. Comput. 31(5), 3744\u20133759 (2009)","journal-title":"SIAM J. Sci. Comput."},{"key":"4_CR25","doi-asserted-by":"publisher","first-page":"1156","DOI":"10.1287\/opre.40.6.1156","volume":"40","author":"B Philippe","year":"1996","unstructured":"Philippe, B., Saad, Y., Stewart, W.J.: Numerical methods in Markov chain modelling. Oper. Res. 40, 1156\u20131179 (1996)","journal-title":"Oper. Res."},{"key":"4_CR26","doi-asserted-by":"crossref","unstructured":"Plateau, B., Stewart, W.J.: Stochastic automata networks. In: Computational Probability, pp. 113\u2013152. Kluwer Academic Press (1997)","DOI":"10.1007\/978-1-4757-4828-4_5"},{"issue":"3","key":"4_CR27","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1016\/j.cam.2011.07.024","volume":"236","author":"I Pultarov\u00e1","year":"2011","unstructured":"Pultarov\u00e1, I., Marek, I.: Convergence of multi-level iterative aggregation-disaggregation methods. J. Comput. Appl. Math. 236(3), 354\u2013363 (2011)","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"4_CR28","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1023\/A:1019120209506","volume":"3","author":"M Sidi","year":"1997","unstructured":"Sidi, M., Starobinski, D.: New call blocking versus handoff blocking in cellular networks. Wirel. Netw. 3(1), 15\u201327 (1997)","journal-title":"Wirel. Netw."},{"key":"4_CR29","volume-title":"Introduction to the Numerical Solution of Markov Chains","author":"WJ Stewart","year":"1994","unstructured":"Stewart, W.J.: Introduction to the Numerical Solution of Markov Chains. Princeton University Press, Princeton (1994)"},{"key":"4_CR30","volume-title":"Multigrid","author":"U Trottenberg","year":"2001","unstructured":"Trottenberg, U., Osterlee, C., Sch\u00fcller, A.: Multigrid. Academic Press, Orlando (2001)"}],"container-title":["Lecture Notes in Computer Science","Computer Performance Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-46433-6_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T01:08:02Z","timestamp":1558314482000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-46433-6_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783319464329","9783319464336"],"references-count":30,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-46433-6_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2016]]},"assertion":[{"value":"16 September 2016","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"EPEW","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"European Workshop on Performance Engineering","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Chios","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Greece","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2016","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"5 October 2016","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"7 October 2016","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"13","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"epew2016","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}