Failure Distance-based Simulation of Repairable Fault-Tolerant Systems

This paper presents a new importance sampling scheme called failure biasing for the efficient simulation of Markovian models of repairable fault-tolerant systems. The new scheme enriches the failure biasing scheme previously proposed by exploiting the concept of failure distance. This results in a much more efficient simulation with speedups over failure biasing of orders of magnitude in typical cases. The paper also discusses the efficient implementation of the new importance sampling scheme and presents a practical method for the optimization of the biasing parameters. NOTE FROM THE AUTHOR: The method proposed in the paper for the optimization of the biasing parameters introduces correlation, making the estimates invalid. A more recent paper, J. A. Carrasco, “Failure Transition Distance-Based Importance Sampling Schemes for the Simulation of Repairable Fault-Tolerant Computer Systems, IEEE Trans. on Reliability, vol. 55, no. 2, June 2006, pp. 207–236, minor corrections in IEEE Trans. on Reliability, vol. 56, no. 2, June 2007. p. 360, presents two slightly modified biasing schemes which can be proved to be more efficient for balanced systems than failure and balanced failure biasing, and describe a correct and efficient method for the optimization of the biasing parameters. The author apologizes for the error in this paper.