Transient analysis of superposed GSPNs

The paper considers transient analysis using randomization for superposed generalized stochastic Petri nets (GSPNs). Since state space explosion implies that space is the bottleneck for numerical analysis, super-posed GSPNs profit from the structured representation known for its associated Markov chain. This moves the bottleneck for analysis from space for generator matrices to space for iteration vectors. Hence a variation of randomization is presented which allows to reduce space requirements for iteration vectors. An additional and welcome side effect is that during an initial phase, this algorithm avoids useless multiplications involving states with zero probability. Furthermore at accommodates to adaptive randomization in a natural way.

[1]  Winfried K. Grassmann.  Transient solutions in markovian queueing systems , 1977, Comput. Oper. Res..

[2]  Gianfranco Ciardo,et al.  Storage Alternatives for Large Structured State Spaces , 1997, Computer Performance Evaluation.

[3]  Brigitte Plateau.  On the stochastic structure of parallelism and synchronization models for distributed algorithms , 1985, SIGMETRICS 1985.

[4]  Giovanni Chiola,et al.  On the Efficient Construction of the Tangible Reachability Graph of Generalized Stochastic Petri Nets , 1987, PNPM.

[5]  Peter Kemper.  Numerical Analysis of Superposed GSPNs , 1996, IEEE Trans. Software Eng..

[6]  Edmundo de Souza e Silva,et al.  State space exploration in Markov models , 1992, SIGMETRICS '92/PERFORMANCE '92.

[7]  Peter Kemper.  Reachability Analysis Based on Structured Representations , 1996, Application and Theory of Petri Nets.

[8]  Kishor S. Trivedi,et al.  Numerical transient analysis of markov models , 1988, Comput. Oper. Res..

[9]  G. Conte,et al.  Parallel State Space Exploration for GSPN Models , 1995, Application and Theory of Petri Nets.

[10]  Edmundo de Souza e Silva,et al.  Performability Analysis of Computer Systems: From Model Spacification to Solution , 1992, Perform. Evaluation.

[11]  Susanna Donatelli,et al.  Superposed Generalized Stochastic Petri Nets: Definition and Efficient Solution , 1994, Application and Theory of Petri Nets.

[12]  A. Jensen,et al.  Markoff chains as an aid in the study of Markoff processes , 1953 .

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

[14]  Harald Stahl,et al.  On the Transient Analysis of Stiff Markov Chains , 1993 .

[15]  Peter W. Glynn,et al.  Computing Poisson probabilities , 1988, CACM.

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

[17]  Kishor S. Trivedi,et al.  Markov and Markov reward model transient analysis: An overview of numerical approaches , 1989 .

[18]  G. Ciardo,et al.  ON THE USE OF KRONECKER OPERATORS FOR THE SOLUTION OF GENERALIZED STOCHASTIC PETRI NETS , 1996 .

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

[20]  Kishor S. Trivedi,et al.  Transient Analysis of Acyclic Markov Chains , 1987, Perform. Evaluation.

[21]  Marco Ajmone Marsan,et al.  Generalized Stochastic Petri Nets: A Definition at the Net Level and Its Implications , 1993, IEEE Trans. Software Eng..

[22]  William H. Sanders,et al.  Empirical Comparison of Uniformization Methods for Continuous-Time Markov Chains , 1995 .

[23]  Marco Ajmone Marsan,et al.  Performance models of multiprocessor systems , 1987, MIT Press series in computer systems.