Circulant approximation for preconditioning in stochastic automata networks

Circulant Approximation for Preconditioning in Stochastic Automata Networks

Stochastic Automata Networks (SANs) are widely used in modeling many practical systems such as queueing systems, communication systems and manufacturing systems. For the performance analysis purposes one needs to calculate the steady state distributions of SANs. Usually, the steady state distributions have no close form solutions and cannot be obtained eeciently by direct methods such as LU dec...

Preconditioning for Stochastic Automata Networks

LANGVILLE, AMY N. Preconditioning for Stochastic Automata Networks. (Under the direction of William J. Stewart.) Many very large Markov chains can be modeled efficiently as Stochastic Automata Networks (SANs). A SAN is composed of individual automata that, for the most part, act independently, requiring only infrequent interaction. SANs represent the generator matrix Q of the underlying Markov ...

Circulant preconditioners for stochastic automata networks

Stochastic Automata Networks (SANs) are widely used in modeling communication systems , manufacturing systems and computer systems. The solution of the steady state distribution cannot be obtained eeciently by direct methods such as LU decomposition due to the huge size of the generator matrix. EEcient numerical algorithm should make use of the tensor structure of SANs' generator matrix. The ge...

Combination of Approximation and Simulation Approaches for Distribution Functions in Stochastic Networks

This paper deals with the fundamental problem of estimating the distribution function (df) of the duration of the longest path in the stochastic activity network such as PERT network. First a technique is introduced to reduce variance in Conditional Monte Carlo Sampling (CMCS). Second, based on this technique a new procedure is developed for CMCS. Third, a combined approach of simulation and ap...

Stochastic Automata Networks