Abstract
In this paper we propose a symbolic method for solving quasi-birth-and-death processes via the RG factorization, and some “simple truncations”—see Remark 4. For reasons yet unexplained, this symbolic method yields the exact G, U, and R matrices in some low dimensional cases like the M/M/c/c retrial queue with c=1,2 servers (these results are essentially known due to Liu and Zhao (2010)), as well as the “Lie solvable model” introduced by Kawanishi (2005) (again only for c=1,2).
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Avram, F., Fotso Chedom, D. On symbolic RG factorization of quasi-birth-and-death processes. TOP 19, 317–335 (2011). https://doi.org/10.1007/s11750-011-0195-7
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DOI: https://doi.org/10.1007/s11750-011-0195-7