{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T06:49:25Z","timestamp":1777099765586,"version":"3.51.4"},"reference-count":49,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T00:00:00Z","timestamp":1776988800000},"content-version":"vor","delay-in-days":113,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Computational and Mathematical Methods"],"published-print":{"date-parts":[[2026,1]]},"abstract":"\n A dynamical system is studied such that belongs to a class of Buslaev nets. This class contains traffic models with complex network structure. We provide results for a more general system than the system that was in consideration earlier. A new version of model has been provided. The studied system contains\n N<\/jats:italic>\n closed curves called circumferences as a topological equivalent. There is a unique common point of the circumferences called the common node. There is a moving segment called a cluster. There may be a delay when a cluster passes through a node. The delay is due to the condition that more than one cluster cannot pass through the node simultaneously. The length of the circumference\n i<\/jats:italic>\n is equal to\n c<\/jats:italic>\n \n i<\/jats:italic>\n <\/jats:sub>\n , the length of the cluster located on this circumference is equal to\n l<\/jats:italic>\n \n i<\/jats:italic>\n <\/jats:sub>\n ,\n i<\/jats:italic>\n = 0, 1, \u22ef,\n N<\/jats:italic>\n \u2212 1. The average distance traveled by a cluster per unit time is called the average cluster velocity. A state of free movement is a state of the system such that all clusters move without delay at the present moment and in the future. Earlier, analytical results were obtained for the system with two circumferences (\n N<\/jats:italic>\n = 2) and the system with circumferences of the same length (\n c<\/jats:italic>\n 0<\/jats:sub>\n =\n c<\/jats:italic>\n 1<\/jats:sub>\n = \u22ef =\n c<\/jats:italic>\n \n N<\/jats:italic>\n \u22121\n <\/jats:sub>\n ). In this paper, the system with any number of circumferences is considered. The lengths of circumferences are different. In traffic models based on exclusion processes, the free movement corresponds to the free\u2010flow phase of traffic flow on a highway. A formula has been obtained for the average cluster velocity under the condition that the system load is sufficiently large, namely, if the condition\n l<\/jats:italic>\n \n i<\/jats:italic>\n <\/jats:sub>\n >\n c<\/jats:italic>\n \n j<\/jats:italic>\n <\/jats:sub>\n \u2212\n l<\/jats:italic>\n \n j<\/jats:italic>\n <\/jats:sub>\n , 0 \u2264\n i<\/jats:italic>\n ,\n j<\/jats:italic>\n \u2264\n N<\/jats:italic>\n \u2212 1, holds. Results regarding ergodicity and invariant measure on the system state space have been obtained.\n <\/jats:p>","DOI":"10.1155\/cmm4\/7261423","type":"journal-article","created":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T06:15:51Z","timestamp":1777097751000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Self\u2010Organization Conditions and Invariant Measure for Traffic Flow on Topological Bouquet With Nonuniform Petals"],"prefix":"10.1155","volume":"2026","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8810-918X","authenticated-orcid":false,"given":"Marina","family":"Yashina","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1921-6579","authenticated-orcid":false,"given":"Jes\u00fas","family":"Vigo-Aguiar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Tatashev","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2026,4,24]]},"reference":[{"key":"e_1_2_13_1_2","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.55.601"},{"key":"e_1_2_13_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(70)90034-4"},{"key":"e_1_2_13_3_2","doi-asserted-by":"publisher","DOI":"10.1051\/jp1:1992277"},{"key":"e_1_2_13_4_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.51.2939"},{"key":"e_1_2_13_5_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1004521326456"},{"key":"e_1_2_13_6_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.62.83"},{"key":"e_1_2_13_7_2","doi-asserted-by":"publisher","DOI":"10.1070\/RM2000v055n03ABEH000295"},{"key":"e_1_2_13_8_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1012202706850"},{"key":"e_1_2_13_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2004.05.015"},{"key":"e_1_2_13_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-004-8822-4"},{"key":"e_1_2_13_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2005.08.005"},{"key":"e_1_2_13_12_2","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/39\/29\/004"},{"key":"e_1_2_13_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-010-9983-y"},{"key":"e_1_2_13_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-014-1089-5"},{"key":"e_1_2_13_15_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202515400011"},{"key":"e_1_2_13_16_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.6237"},{"key":"e_1_2_13_17_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-023-03190-8"},{"key":"e_1_2_13_18_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.46.R6124"},{"key":"e_1_2_13_19_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.60.5301"},{"key":"e_1_2_13_20_2","doi-asserted-by":"publisher","DOI":"10.1214\/ECP.v10-1148"},{"key":"e_1_2_13_21_2","unstructured":"AustinT. 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