Genetic algorithms for the identification of the generalised Erlang laws parameters used in systems dependability studies

Abstract

In systems dependability modelling, the absence of a fine knowledge on the failure dynamics for certain systems and on the multiple interactions which exist between the various subsystems, and also the difficulty to validly use some simplifying assumptions require to resort with the exploitation of experience feedback. In addition, one has approximate models and, the problem is then to find the parameters of these models which satisfy “as well as possible” the observed feedback data, according to the principle of maximum of probability or minimum of least squares (it depends on the nature of the obtained data). Certain identification heuristics were hitherto used, but they showed their limits when, for instance, the relief of the function to be optimised presents many local valleys. These difficulties led us to consider an approach totally different where the transition rules can allow to avoid local cavities. For that, we studied a certain number of operational research techniques and finally chose a resolution by genetic algorithms. Their major advantage is that they operate the search of an optimum starting from a population and not from only one single point, allowing thus a parallel search, effective on the whole solutions space. After a thorough presentation of the considered applicability and the obtained results in this study, we underline in this communication the observed advantages, difficulties and limits compared to more traditional techniques for the parametric identification.