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

Florin Avram (1) , D. Fotso Chedom

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

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). © 2011 Sociedad de Estadística e Investigación Operativa.

Domaines: Probabilités [math.PR]

Florin Avram, D. Fotso Chedom. On symbolic RG factorization of quasi-birth-and-death processes. TOP, 2011, 19 (2), pp.317-335. ⟨10.1007/s11750-011-0195-7⟩. ⟨hal-00865054⟩