On the canonical representation of phase type distributions

Gabor, Horvath [Horváth, Gábor (Tömegkiszolgálás), szerző] Híradástechnikai Tanszék (BME / VIK); Miklos, Telek [Telek, Miklós (Sztochasztikus mo...), szerző] Híradástechnikai Tanszék (BME / VIK)

Angol nyelvű Tudományos Szakcikk (Folyóiratcikk)
Megjelent: PERFORMANCE EVALUATION 0166-5316 1872-745X 66 (8) pp. 396-409 2009
  • SJR Scopus - Computer Networks and Communications: Q1
    The characterization and the canonical representation of order-n phase type distributions (PH(n)) is an open research problem. This problem is solved for n = 2, since the equivalence of the acyclic and the general PH distributions has been proven for a long time. However, no canonical representations have been introduced for the general PH distribution class so far for n > 2. In this paper, we summarize the related results for n = 3. Starting from these results we provide a canonical representation of the PH(3) class (that is a minimal representation, too) and present a symbolical transformation procedure to obtain the canonical representation based on any (not only Markovian) vector-matrix representation of the distribution. We show that - using the same approach - no symbolical results can be derived for the order-4 PH distributions, thus probably the PH(3) class is the highest order PH class for which a symbolical canonical transformation exists. Using the transformation method to canonical form for PH(3) we numerically evaluate the moment bounds of the PH(3) distribution set, compare it to the order-3 acyclic PH distribution (APH(3)) class, and present other possible applications of the canonical form. (C) 2008 Elsevier B.V. All rights reserved.
    Hivatkozás stílusok: IEEEACMAPAChicagoHarvardCSLMásolásNyomtatás
    2021-08-03 13:45