Abstract
The compositional representation of a Markov chain using Kronecker algebra, according to a compositional model representation as a superposed generalized stochastic Petri net or a stochastic automata network, has been studied for a while. In this paper we describe a generalized Kronecker structure, and its implementation, which is able to handle synchronization over activities of different levels of priority. The achieved Kronecker structure serves for functional analysis as well as performance analysis based on Markov chains.
This research is partially supported by CNR Short-term Mobility program and Deutsche Forschungsgemeinschaft, SFB 559.
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References
M. Ajmone Marsan, G. Balbo, G. Conte, S. Donatelli, and G. Franceschinis. Modelling with Generalized Stochastic Petri Nets. J. Wiley, 1995.
G. Balbo, G. Chiola, G. Franceschinis, and G. Molinar-Roet. On the efficient construction of the tangible reachability graph of generalized stochastic Petri nets. In Proc. 2nd int. Work. Petri Nets and Performance Models, Madison (USA) 1987, IEEE Computer Society.
F. Bause, P. Buchholz, and P. Kemper. A toolbox for functional and quantitative analysis of DEDS (extended abstract). In Proc. 10th int. Conf. Computer Performance Evalutation, Modelling Techniques and Tools, LNCS 1469, Springer, 1998.
O. Botti, S. Donatelli, and G. Franceschinis. Assessing the performance of multi-processor architectures through SWN models simulation: a case study in the field of plant automation systems. In Proc. 29th Annual Simulation Symposium, New Orleans, Louisiana, April 8–11, 1996, IEEE-CS Press.
P. Buchholz, G. Ciardo, S. Donatelli, and P. Kemper. Complexity of Kronecker operations on sparse matrices with applications to the solution of Markov models. ICASE Report No. 97-66 NASA/CR-97-206274, 1997. To appear in Informs Journal on Computing.
P. Buchholz, P. Kemper. Modular state level analysis of distributed systems-techniques and tool suppport. In Proc. 5th Int. Conf. Tools and Algorithms for the Construction and Analysis of Systems, Springer LNCS 1579, 1999.
G. Chiola, S. Donatelli, and G. Franceschinis. GSPN versus SPN: what is the actual role of immediate transitions?, In Proc. 4th int. Conf. Petri Nets and Performance Models, Melbourne, Australia, December 1991.
G. Chiola, G. Franceschinis, R. Gaeta, and M. Ribaudo. GreatSPN 1.7: GRaphical Editor and Analyzer for Timed and Stochastic Petri Nets. Performance Evaluation, special issue on Performance Modelling Tools, (1), 24, 1996.
P. Buchholz and P Kemper. Efficient computation and representation of large reachability sets for composed automata. Forschungsbericht 705, Fachbereich Informatik, Universität Dortmund (Germany), 1999.
J. Campos, S. Donatelli, and M. Silva. Structured solution of asynchronously communicating stochastic modules. IEEE Trans. on Software Engineering, 25(2).
G. Ciardo and A. Miner. A data structure for the efficient Kronecker solution of GSPNs. In Proc. 8th int. Work. Petri Nets and Performance Models, IEEE CS Press, 1999.
G. Ciardo and A. Miner. Efficient reachability set generation and storage using decision diagrams. In Proc. 20th int. Conf. Application and Theory of Petri Nets, LNCS 1639, Springer, 1999.
G. Ciardo and M. Tilgner. On the use of Kronecker operators for the solution of generalized stochastic Petri nets. ICASE Report 96-35, Institute for Computer Applications in Science and Engineering, Hampton, VA, May 1996.
M. Davio. Kronecker products and shuffle algebra. IEEE Transactions on Computers, 30(2):116–125, 1981.
S. Donatelli. Superposed generalized stochastic Petri nets: definition and efficient solution. In Proc. 15th int. Conf. Application and Theory of Petri Nets LNCS 815, Springer 1994.
T. Kam. State minimization of finite state machines using implicit techniques. Phd thesis, University of California at Berkeley, 1995.
P. Kemper. Numerical analysis of superposed GSPNs. IEEE Trans. on Software Engineering, 22(9), Sep 1996.
P. Kemper. Reachability analysis based on structured representations. In Proc. 17th int. Conf. Application and Theory of Petri Nets, LNCS 1091. Springer, 1996.
B. Plateau. On the stochastic structure of parallelism and synchronisation models for distributed algorithms. In Proc. 1985 ACM SIGMETRICS Conf. on Measurement and Modeling of Computer Systems, Austin, TX, USA, May 1985.
M. Tilgner, Y. Takahashi, and G. Ciardo. SNS: synchronized network solver. In M. Silva, R. Valette and K. Takahashi (eds.), Work. Manufacturing and Petri nets, within 17th int. Conf. Application and Theory of Petri nets, Osaka, Japan, 1996.
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Donatelli, S., Kemper, P. (2000). Integrating Synchronization with Priority into a Kronecker Representation. In: Haverkort, B.R., Bohnenkamp, H.C., Smith, C.U. (eds) Computer Performance Evaluation.Modelling Techniques and Tools. TOOLS 2000. Lecture Notes in Computer Science, vol 1786. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46429-8_15
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DOI: https://doi.org/10.1007/3-540-46429-8_15
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