On symbolic RG factorization of quasi‐birth‐and‐death processes

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).