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

• Florin Avram ^[1] ; Donatien Fotso Chedom ^[2]
  1. [1] University of Pau and Pays de l'Adour

     University of Pau and Pays de l'Adour

     Arrondissement de Pau, Francia

     
  2. [2] Université de Yaoundé I, Camerún
• Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 19, Nº. 2, 2011, págs. 317-335
• Idioma: inglés
• DOI: 10.1007/s11750-011-0195-7
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• Resumen

  • 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).