Stochastic Automata Networks

A Stochastic Automata Network (SAN) consists of a number of individual stochastic automata that operate more or less independently of each other. Each individual automaton, A, is represented by a number of states and rules that govern the manner in which it moves from one state to the next. The state of an automaton at any time t is just the state it occupies at time t and the state of the SAN at time t is given by the state of each of its constituent automata.

[1]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[2]  William Henderson,et al.  Aggregation and Disaggregation Through Insensitivity in Stochastic Petri Nets , 1993, Perform. Evaluation.

[3]  William J. Stewart,et al.  A Simultaneous Iteration Algorithm for Real Matrices , 1981, TOMS.

[4]  C. Berge Graphes et hypergraphes , 1970 .

[5]  Dirk Frosch Product Form Solutions for Closed Synchronized Systems of Stochastic Sequential Processes , 1992, Universität Trier, Mathematik/Informatik, Forschungsbericht.

[6]  G. Stewart Simultaneous iteration for computing invariant subspaces of non-Hermitian matrices , 1976 .

[7]  Jean-Michel Fourneau,et al.  PEPS: A Package for Solving Complex Markov Models of Parallel Systems , 1989 .

[8]  Brigitte Plateau,et al.  Numerical Issues for Stochastic Automata Networks , 1996 .

[9]  Giovanni Chiola,et al.  Stochastic Well-Formed Colored Nets and Symmetric Modeling Applications , 1993, IEEE Trans. Computers.

[10]  Peter G. Taylor,et al.  Embedded Processes in Stochastic Petri Nets , 1991, IEEE Trans. Software Eng..

[11]  Y. Saad Krylov subspace methods for solving large unsymmetric linear systems , 1981 .

[12]  Thomas G. Robertazzi,et al.  Markovian Petri Net Protocols with Product Form Solution , 1991, Perform. Evaluation.

[13]  Matteo Sereno,et al.  On the Product Form Solution for Stochastic Petri Nets , 1992, Application and Theory of Petri Nets.

[14]  A. Jennings,et al.  Simultaneous Iteration for Partial Eigensolution of Real Matrices , 1975 .

[15]  P. Buchholz Equivalence Relations for Stochastic Automata Networks , 1995 .

[16]  William J. Stewart,et al.  Introduction to the numerical solution of Markov Chains , 1994 .

[17]  Rais Gatic Bukharaev Theorie der stochastischen Automaten , 1995, Leitfäden der Informatik.

[18]  Richard J. Boucherie A Characterization of Independence for Competing Markov Chains with Applications to Stochastic Petri Nets , 1994, IEEE Trans. Software Eng..

[19]  Wei Wu,et al.  Numerical Experiments with Iteration and Aggregation for Markov Chains , 1992, INFORMS J. Comput..

[20]  T. Y. WilliamJ,et al.  Numerical Methods in Markov Chain Modeling , 1992, Operational Research.

[21]  Karim Atif Modélisation du parallélisme et de la synchronisation , 1992 .

[22]  Jean-Michel Fourneau,et al.  Graphs and Stochastic Automata Networks , 1995 .

[23]  Paulo Fernandes,et al.  Efficient descriptor-vector multiplications in stochastic automata networks , 1998, JACM.

[24]  W. Arnoldi The principle of minimized iterations in the solution of the matrix eigenvalue problem , 1951 .

[25]  Matteo Sereno,et al.  Arrival Theorems for Product-Form Stochastic Petri Nets , 1994, SIGMETRICS.

[26]  William H. Sanders,et al.  Reduced base model construction methods for stochastic activity networks , 1989, Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89.

[27]  William J. Stewart,et al.  Numerical Solution of Markov Chains , 1993 .

[28]  Brigitte Plateau,et al.  On the stochastic structure of parallelism and synchronization models for distributed algorithms , 1985, SIGMETRICS '85.

[29]  Brigitte Plateau,et al.  Stochastic Automata Network For Modeling Parallel Systems , 1991, IEEE Trans. Software Eng..

[30]  Gunther Schmidt,et al.  Relations and Graphs , 1993, EATCS Monographs on Theoretical Computer Science.

[31]  FernandesPaulo,et al.  Efficient descriptor-vector multiplications in stochastic automata networks , 1998 .

[32]  H. Hermanns,et al.  Syntax , Semantics , Equivalences , and Axioms for MTIPP y , 1994 .

[33]  Jean-Michel Fourneau,et al.  A Methodology for Solving Markov Models of Parallel Systems , 1991, J. Parallel Distributed Comput..

[34]  Marco Ajmone Marsan,et al.  The Application of EB-Equivalence Rules to the Structural Reduciton of GSPN Models , 1992, J. Parallel Distributed Comput..

[35]  J. Hillston Compositional Markovian Modelling Using a Process Algebra , 1995 .

[36]  Anthony Unwin,et al.  Reversibility and Stochastic Networks , 1980 .

[37]  Giuliana Franceschinis,et al.  Computing Bounds for the Performance Indices of Quasi-Lumpable Stochastic Well-Formed Nets , 1994, IEEE Trans. Software Eng..

[38]  Peter Buchholz Aggregation and reduction techniques for hierarchical GCSPNs , 1993, Proceedings of 5th International Workshop on Petri Nets and Performance Models.

[39]  Marc Davio,et al.  Kronecker products and shuffle algebra , 1981, IEEE Transactions on Computers.

[40]  J. Meyer The Role of the Group Generalized Inverse in the Theory of Finite Markov Chains , 1975 .

[41]  Susanna Donatelli,et al.  Superposed Stochastic Automata: A Class of Stochastic Petri Nets with Parallel Solution and Distributed State Space , 1993, Perform. Evaluation.

[42]  W. Stewart,et al.  The numerical solution of stochastic automata networks , 1995 .

[43]  Peter Kemper Closing the Gap Between Classical and Tensor Based Iteration Techniques , 1995 .

[44]  Y. Saad Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices , 1980 .

[45]  J. H. Wilkinson The algebraic eigenvalue problem , 1966 .