Geodesic
Multitype branching processes with immigration in random environment, and polling systems
Matematičeskie trudy, Tome 14 (2011) no. 1, pp. 3-49

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For multitype branching processes with immigration evolving in a random environment and producing a final product, we find the tail distribution of the size of the final product accumulated in the process for a life period. Using this result, we investigate the tail distributions of the busy periods of the queueing polling systems of branching type with random service disciplines and random positive switch-over times. 
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     author = {V. A. Vatutin},
     title = {Multitype branching processes with immigration in random environment, and polling systems},
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V. A. Vatutin. Multitype branching processes with immigration in random environment, and polling systems. Matematičeskie trudy, Tome 14 (2011) no. 1, pp. 3-49. http://geodesic.mathdoc.fr/item/MT_2011_14_1_a0/