{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T10:10:34Z","timestamp":1773655834401,"version":"3.50.1"},"reference-count":15,"publisher":"Allerton Press","issue":"1","license":[{"start":{"date-parts":[[2011,2,1]],"date-time":"2011-02-01T00:00:00Z","timestamp":1296518400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2011,2,1]],"date-time":"2011-02-01T00:00:00Z","timestamp":1296518400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Aut. Conrol Comp. Sci."],"published-print":{"date-parts":[[2011,2]]},"DOI":"10.3103\/s0146411611010044","type":"journal-article","created":{"date-parts":[[2011,3,19]],"date-time":"2011-03-19T04:29:48Z","timestamp":1300508988000},"page":"29-38","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Invariance of the stationary state distribution for mass service networks with multi-regime strategies, different demands, and a \u201cgeneralized processor sharing\u201d discipline"],"prefix":"10.3103","volume":"45","author":[{"given":"A. R.","family":"Eremina","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1627","published-online":{"date-parts":[[2011,3,20]]},"reference":[{"issue":"1","key":"6125_CR1","first-page":"106","volume":"2","author":"B.A. Sevast\u2019yanov","year":"1957","unstructured":"Sevast\u2019yanov, B.A., Limit Theorem for Markov Processes and Its Application to Telephone Systems with Rejections, Teor. Veroyat. Prim., 1957, vol. 2, no. 1, pp. 106\u2013116.","journal-title":"Teor. Veroyat. Prim."},{"key":"6125_CR2","unstructured":"Kovalenko, I.N., About One Method in the Theory of Mass Service, Trudy VI Vses. soveshchaniya po teorii veroyatnostej i mat. statistike, (Proc. VI All-Un. Conf. on Theory of Probabilities and Math. Statistics), Vilnus, 1962, pp. 357\u2013358."},{"key":"6125_CR3","volume-title":"Issledovaniya po analizu nadezhnosti slozhnykh sistem","author":"I.N. Kovalenko","year":"1976","unstructured":"Kovalenko, I.N., Issledovaniya po analizu nadezhnosti slozhnykh sistem (Studies of Analysis of Complex System Reliability), Kiev: Naukova Dumka, 1976."},{"key":"6125_CR4","volume-title":"Itogi nauki i tekhniki. Teoriya veroyatnostei. Mat. statistika. Teoretich. kibernetika. T. 18","author":"D. Kenig","year":"1981","unstructured":"Kenig, D., Rykov, V.V., and Shmidt, F., Stationary Systems of Mass Service with Dependences, in Itogi nauki i tekhniki. Teoriya veroyatnostei. Mat. statistika. Teoretich. kibernetika. T. 18 (Resume of Science and Technics. Theory of Probabilities. Mathematical Statistics. Theoretical Cybernetics. Vol. 18), Moscow: VINITI, 1981."},{"issue":"2","key":"6125_CR5","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1145\/321879.321887","volume":"22","author":"F. Baskett","year":"1975","unstructured":"Baskett, F., Chandy, K. M., Muntz, R.R., and Palacios, F.G., Open, Closed and Mixed Networks of Queues with Different Classes of Customers, J. Assoc. Comput. Mach., 1975, vol. 22, no. 2, pp. 248\u2013260.","journal-title":"J. Assoc. Comput. Mach."},{"issue":"1","key":"6125_CR6","first-page":"135","volume":"14","author":"D. Stoyan","year":"1978","unstructured":"Stoyan, D., Queuing Networks Insensivity and Heuristic Approximation, Electron. Information. Kibern., 1978, vol. 14, no. 1, pp. 135\u2013143.","journal-title":"Electron. Information. Kibern."},{"issue":"3","key":"6125_CR7","first-page":"385","volume":"16","author":"U. Jansen","year":"1980","unstructured":"Jansen, U. and Konig, D., Insensivity and Steady-State Probabilities in Product Form for Queuing Networks, Electron. Information. Kibern., 1980, vol. 16, no. 3, pp. 385\u2013397.","journal-title":"Electron. Information. Kibern."},{"issue":"1","key":"6125_CR8","first-page":"188","volume":"27","author":"V.A. Ivnitskii","year":"1982","unstructured":"Ivnitskii, V.A., On the Condition of Invariance of Stationary Probabilities for Mass Service Networks, Teoriya Veroyat. Primen., 1982, vol. 27, no. 1, pp. 188\u2013192.","journal-title":"Teoriya Veroyat. Primen."},{"key":"6125_CR9","volume-title":"Teoriya setei massovogo obsluzhivaniya","author":"V.A. Ivnitskii","year":"2004","unstructured":"Ivnitskii, V.A., Teoriya setei massovogo obsluzhivaniya (Theory of Mass Service Networks), Moscow: Fizmatlit, 2004."},{"key":"6125_CR10","unstructured":"Kovalev, E.A., Networks with Unreliable Channels and Reserve, Materialy VI Bel. shkoly-seminara po TMO \u201cMatematicheskie metody issledovaniya setei svyazi i setei EVM\u201d (Proc. VI Belgor. School-Semin. on Theory of Mass Service, Mathematical Methods of Connection Networks and Computer Networks), Minsk, 1990, pp. 70\u201371."},{"key":"6125_CR11","unstructured":"Malinkovskii, Yu.V. and Nueman, A.Yu., Closed Information Networks with Multimode Strategies of Service, Materialy I mezhdunarodnoi konferentsii \u201cInformatsionnye sistemy i tekhnologii\u201d (ISTKh2002) (Proc. I Int. Conf. Information Systems and Technologies), Minsk, 2002, part 1."},{"key":"6125_CR12","unstructured":"Malinkovskii, Yu.V. and Nueman, A.Yu., Multiplikativity of Stationary Distribution in Open Networks with Multimode Strategies of Service, Vesti NANB. Ser. Fiz.-Mat. Navuk, 2001, no. 3, pp. 129\u2013134."},{"key":"6125_CR13","unstructured":"Starovoitov, A.N., Invariance of Stationary Distribution in Networks with Multimode Strategies of Service and PS Service Discipline, Materialy IX Respubl. Nauchn. Konf. Stud. i Aspir. \u201cNovye Mat. Metody i Komp\u2019yuternye Tekhnologii v Proektirovanii, Proizvodstvennykh i Nauchnykh Issledovaniyakh\u201d (Proc. IX Rep. Sci. Conf. St. Postgrad. St. Mew Math. Methods Comp. Technol. in Design, Industry and Sci. Studies), Gomel\u2019, 2006, pp. 199\u2013200."},{"key":"6125_CR14","unstructured":"Malinkovskii, Yu.V., Starovoitov, A.N., and Eremina, A.R., Starovoitov, A.N., Invariance of Stationary Distribution of Probabilities of State of Networks with Multimode Strategies of Service, Claims of Different Types and LSFS RR Service Discipline, Vestnik Tomsk. Gos. Univ. Upravl., Vych. Tekhn. Inform., 2009, no. 3(8), pp. 33\u201339."},{"key":"6125_CR15","unstructured":"Letunovich, Yu.E., Stationary Distribution of States of Open Inhomogeneous Network with Multimode Strategies and Immediate Service, Sb. Nauch. St. Konf. \u201cSovremennye Informatsionnye Komp\u2019yuternye Tekhnologii\u201d (Proc. Conf. Contemp. Inform. Comp. Techn.), Grodno, 2008, pp. 97\u201399."}],"container-title":["Automatic Control and Computer Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.3103\/S0146411611010044.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.3103\/S0146411611010044","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.3103\/S0146411611010044","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.3103\/S0146411611010044.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T21:59:46Z","timestamp":1773611986000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.3103\/S0146411611010044"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,2]]},"references-count":15,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,2]]}},"alternative-id":["6125"],"URL":"https:\/\/doi.org\/10.3103\/s0146411611010044","relation":{},"ISSN":["0146-4116","1558-108X"],"issn-type":[{"value":"0146-4116","type":"print"},{"value":"1558-108X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,2]]},"assertion":[{"value":"1 October 2010","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 November 2010","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 March 2011","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}