Aggregation of stochastic automata networks with replicas

On the Relationships Between Lumpability and Filtering of Finite Stochastic Systems

“…see the recent papers [9,14,2,20]). This is specially true in performance evaluation, where various modelling formalisms (e.g.…”

Modular Analytical Performance Models for Ad Hoc Wireless Networks

“…1 (2) e2(π2) e5 1 presents a SAN model with two automata, four local events, one synchronizing event, and one functional rate. In the context of this paper, we will use roman letters to identify the name of events and functions, and greek letters to describe constant values of rates and probabilities.…”

“…The modular approach allowed by SAN brings further advantages that lie not only in the size of the models that can be analyzed, if compared to MC, but also in the possibility of stepwise representing aspects of the reality of interest and analyzing the numerical results associated [8,2]. In fact, the use of the SAN formalism attenuates the state space problem by furnishing efficient numerical methods to compute performance indices.…”

Performance analysis issues for parallel implementations of propagation algorithm

“…If automaton A (1) is in state 1 (1) , the transition from state 0 (2) to 1 (2) does not occur (rate equal to 0). Using the SAN notation employed by the software tool PEPS2003 [3], the expression of this function is:…”

“…The use of functional transitions is a powerful primitive of the SAN formalism, since it allows to describe very complex behaviors in a very compact format. The computational costs to handle functional rates has decreased significantly with the developments of numerical solutions for SAN models, e.g., the algorithms for generalized tensor products [2,5]. Table 2.…”