Browsing by Subject "Stochastic Automata Networks"

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Open Access
Iterative methods based on splittings for stochastic automata networks
(1998) Uysal, E.; Dayar T.
This paper 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. With 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 could be solved by explicitly storing the global generator in the core of a target architecture especially if the generator is reasonably dense. © 1998 Elsevier Science B.V. All rights reserved.
Open Access
Lumpable continuous-time stochastic automata networks
(Elsevier, 2003-07-16) Gusak, O.; Dayar, T.; Fourneau, J. M.
The generator matrix of a continuous-time stochastic automata network (SAN) is a sum of tensor products of smaller matrices, which may have entries that are functions of the global state space. This paper specifies easy to check conditions for a class of ordinarily lumpable partitionings of the generator of a continuous-time SAN in which aggregation is performed automaton by automaton. When there exists a lumpable partitioning induced by the tensor representation of the generator, it is shown that an efficient aggregation-iterative disaggregation algorithm may be employed to compute the steady-state distribution. The results of experiments with two SAN models show that the proposed algorithm performs better than the highly competitive block Gauss-Seidel in terms of both the number of iterations and the time to converge to the solution. © 2002 Elsevier Science B.V. All rights reserved.
Open Access
Stochastic automata networks and near complete decomposability
(SIAM, 2002) Gusak, O.; Dayar T.; Fourneau, J. M.
Stochastic automata networks (SANs) have been developed and used in the last fifteen years as a modeling formalism for large systems that can be decomposed into loosely connected components. In this work, we extend the near complete decomposability concept of Markov chains (MCs) to SANs so that the inherent difficulty associated with solving the underlying MC can be forecasted and solution techniques based on this concept can be investigated. A straightforward approach to finding a nearly completely decomposable (NCD) partitioning of the MC underlying a SAN requires the computation of the nonzero elements of its global generator. This is not feasible for very large systems even in sparse matrix representation due to memory and execution time constraints. We devise an efficient decompositional solution algorithm to this problem that is based on analyzing the NCD structure of each component of a given SAN. Numerical results show that the given algorithm performs much better than the straightforward approach.