R. Marie and B. Sericola, \Distribution du temps total de sejour dans un sous-ensemble d' etats transitoires d'un processus Markovien homogene a espace d'etat ni," Rapport 585, INRIA, Rennes, France, Nov. 1986. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Performability Analysis Using semi-Markov reward processes - Ciardo, Marie, Sericola.. (1990) (7 citations) Self-citation (Marie Sericola) (Correct)
....before the underlying stochastic process can be studied: a GSPN is hence transformed into a smaller Markov chain whose states are the tangible markings only. Yet another related e ort is reported in [11] where groups of fast states are approximated to be groups of vanishing states. In [12], the distribution of sojourn time until absorption for a given subset of states in a Markov process is calculated. In gure 1, state recover becomes vanishing if is 0. This would amount to saying that no useful work is performed when a recovery is under way, a reasonable assumption. 4 The De ....
....by the two processes respectively, including the initial state. We then obtain the following results: N(1) 0g = prf X 0 2 SA g = 1 1 = 8n 1; prf N(1) ng = n 1 where 1 is the column vector with all entries equal to 1. The following results are proved in [12]: 8i 2 S 1 ; 8n 0; prfN(1) n j X 0 = ig = prf 8i 2 S 0 ; 8n 0; prfN(1) n j X 0 = ig = M i;j prfN(1) n j X 0 = jg 8n 0; prfN(1) ng = prf N(1) ng Using the above de nitions and results, the following lemmas are proved (in the appendix) Lemma 1 (dealing with the case ....
R. Marie and B. Sericola, \Distribution du temps total de sejour dans un sous-ensemble d' etats transitoires d'un processus Markovien homogene a espace d'etat ni," Rapport 585, INRIA, Rennes, France, Nov. 1986.
Performability Analysis Using semi-Markov reward processes - Ciardo, Marie, Sericola.. (1990) (7 citations) Self-citation (Marie Sericola) (Correct)
....before the underlying stochastic process can be studied: a GSPN is hence transformed into a smaller Markov chain whose states are the tangible markings only. Yet another related effort is reported in [11] where groups of fast states are approximated to be groups of vanishing states. In [12], the distribution of sojourn time until absorption for a given subset of states in a Markov process is calculated. In figure 1, state recover becomes vanishing if fl is 0. This would amount to saying that no useful work is performed when a recovery is under way, a reasonable assumption. 4 The ....
....initial state. We then obtain the following results: prf N(1) 0g = prf X 0 2 SA g = 1 Gamma [T ] 1 = A] 1 8n 1; prf N(1) ng = T ] P [T T ] n Gamma1 P [T A] 1 where 1 is the column vector with all entries equal to 1. The following results are proved in [12]: 8i 2 S 1 ; 8n 0; prfN(1) n j X 0 = ig = prf N(1) n j X 0 = ig 8i 2 S 0 ; 8n 0; prfN(1) n j X 0 = ig = X j2S 1 M i;j prfN(1) n j X 0 = jg 8n 0; prfN(1) ng = prf N(1) ng Using the above definitions and results, the following lemmas are proved (in the appendix) ....
R. Marie and B. Sericola, "Distribution du temps total de s'ejour dans un sous-ensemble d' 'etats transitoires d'un processus Markovien homog`ene `a espace d"etat fini," Rapport 585, INRIA, Rennes, France, Nov. 1986.
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