Graphs and Stochastic Automata Networks

1995 ◽  
pp. 217-235 ◽  
Author(s):  
Jean-Michel Fourneau ◽  
Franck Quessette
Keyword(s):  
Stochastic Automata ◽  
Automata Networks

scholarly journals Multipreconditioned GMRES for simulating stochastic automata networks

2018 ◽  
Vol 16 (1) ◽  
pp. 986-998
Author(s):  
Chun Wen ◽  
Ting-Zhu Huang ◽  
Xian-Ming Gu ◽  
Zhao-Li Shen ◽  
Hong-Fan Zhang ◽  
...  
Keyword(s):  
Steady State ◽  
Probability Distribution ◽  
Linear Systems ◽  
Iterative Methods ◽  
Communication Systems ◽  
Queueing Systems ◽  
Steady State Probability ◽  
Stochastic Automata ◽  
Automata Networks ◽  
Generator Matrices

AbstractStochastic Automata Networks (SANs) have a large amount of applications in modelling queueing systems and communication systems. To find the steady state probability distribution of the SANs, it often needs to solve linear systems which involve their generator matrices. However, some classical iterative methods such as the Jacobi and the Gauss-Seidel are inefficient due to the huge size of the generator matrices. In this paper, the multipreconditioned GMRES (MPGMRES) is considered by using two or more preconditioners simultaneously. Meanwhile, a selective version of the MPGMRES is presented to overcome the rapid increase of the storage requirements and make it practical. Numerical results on two models of SANs are reported to illustrate the effectiveness of these proposed methods.

scholarly journals Iterative disaggregation for a class of lumpable discrete-time stochastic automata networks

2003 ◽  
Vol 53 (1) ◽  
pp. 43-69 ◽  
Author(s):  
Oleg Gusak ◽  
Tuğrul Dayar ◽  
Jean-Michel Fourneau
Keyword(s):  
Discrete Time ◽  
Stochastic Automata ◽  
Automata Networks
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