Abstract
The paper concerns the possibilities for mathematical modelling of safety related systems (equipment oriented on safety). Some mathematical models have been required by the present European Standards for the railway transport. We are interested in the possibility of using Markov's models to meet these Standards. In the text an example of using that method in the interlocking equipment life cycle is given. An efficient aggregation/disaggregation method for computing some characteristics of Markov chains is presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. Ciardo, A. Blakmore, P. F. Chimento, JR., J. K. Muppala and K. S. Trivedi: Automated generation and analysis of Markov reward models using stochastic reward nets. In: Linear Algebra, Markov Chain, and Queueing Models (C.D. Meyer, R. J. Plemmons, eds.). Springer-Verlag, New York, 1993, pp. 145–191.
R. David, H. Alla: Petri Nets and Grafcet: Tools for Modelling Discrete Event Systems. Prentice Hall International, 1992.
B.W. Johnson: Design and Analysis of Fault-Tolerant Digital Systems. Addison-Wesley Publishing Company, Massachusetts, 1989.
Š. Klapka, P. Mayer: Some aspects of modelling railway safety. In: Proceedings of the XIIIth SANM, Ne?tiny. Západo?eská univerzita, Plze?, 1999, pp. 135–140.
K. Kule: Reliability and safety of interlocking systems. NADAS, Praha, 1980. (In Czech.)
I. Marek, P. Mayer: Convergence analysis of an iterative aggregation/disaggregation method for computing stationary probability vectors of stochastic matrices. Numer. Linear Algebra Appl. 5 (1998), 253–274.
I. Marek, P. Mayer: Iterative aggregation/disaggregation methods for computing stationary probability vectors of stochastic matrices can be finitely terminating. J. Differential Equations 3 (2001), 301–313.
M. Ajmone Marsan, G. Balbo, G. Conte, S. Donatelli and G. Franceschinis: Modelling with Generalized Stochastic Petri Nets. John Wiley & Sons, Chichester, 1995.
B. Plateau, K. Atif: Stochastic automata network for modelling parallel systems. IEEE transaction on software engineering 17 (1991), 1093–1108.
K. Rásto?ný: Models for analysis of safety computer interlocking systems. Habilitation thesis. University of Žilina, 1998. (In Slovak.)
W. J. Stewart: Introduction to the Numerical Solution of Markov Chains. Princeton University Press, Princenton, 1994.
J. Walter: Stochastic Models in Economy. SNTL, Praha, 1970. (In Czech.)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Klapka, S., Mayer, P. Aggregation/Disaggregation Method for Safety Models. Applications of Mathematics 47, 127–137 (2002). https://doi.org/10.1023/A:1021733118228
Issue Date:
DOI: https://doi.org/10.1023/A:1021733118228