Browsing by Subject "Stochastic automata networks"
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Item Open Access Effects of reordering and lumping in the analysis of discrete-time sans(Birkhäuser, Basel, 2000) Dayar, Tuğrul; Gardy, D.; Mokkadem, A.In a recent paper [13],it is shown that discrete-time stochastic automata networks (SANs) are lumpable under rather general conditions. Therein, the authors present an efficient iterative aggregation-disaggregation (IAD) algorithm geared towards computing the stationary vector of discrete-time SANs that satisfy the conditions of lumpability. The performance of the proposed IAD solver essentially depends on two parameters. The first is the order in which the automata are lined up, and the second is the size of the lumped matrix. Based on the characteristics of the SAN model at hand, the user may have some flexibility in the choice of these two parameters. In this paper, we give rules of thumb regarding the choice of these parameters on a model from mobile communications.Item Open Access Iterative methods based on splittings for stochastic automata networks(Bilkent University, 1997) Uysal, ErtuğrulThis thesis presents iterative methods based on splittings (Jacobi, Gauss-Seidel, Successive Over Relaxation) and their block versions for Stochastic Automata Networks (SANs). These methods prove to be better than the power method that has been used to solve SANs until recently. Through the help of three examples we show that the time it takes to solve a system modeled as a SAN is still substantial and it does not seem to be possible to solve systems with tens of millions of states on standard desktop workstations with the current state of technology. However, the SAN methodology enables one to solve much larger models than those that could be solved by explicitly storing the global generator in the core of a target architecture especially if the generator is reasonably dense.