Fault Injection Simulation: A Variance Reduction Technique For Systems With Rare Events

Performability modelling has been most successfully applied for gracefully degradable computer systems by using Markov reward models [2]. In this approach the relation of the performability model with the underlying performance and dependability model is exploited. For many systems and for many measures of interest this type of modelling is not suited, so another performability modelling approach is necessary. In this paper we introduce Fault Injection Simulation (FIS), a modelling approach which can be used to evaluate highly dependable systems with very small failure rates. In this respect one can for instance think of the very small token loss probabilities in the high speed FDDI token ring. FIS decomposes a realization of a Discrete Event Dynamic System [3] in a fault affected and a nonaffected part. For these two parts steady-state measures are derived and weighted to calculate the desired overall steady-state measure. The individual measures can be obtained by analytical or numerical means or by simulation. In many cases analytical or numerical methods will not be available in which case FIS is a pure fast simulation technique. In this paper we will concentrate on the use of FIS as a pure simulation method. When one wants accurate simulation results in a reasonable time span for systems that are strongly influenced by rarely occurring events the use of variance reduction techniques (e.g. [3], [4]) is inevitable. Otherwise far too much time is needed before enough of these events are simulated. It seems FIS can compete with other known techniques in ease of applicability and amount of variance reduction. This paper is organized as follows. In Section 2 we informally introduce FIS. In Section 3 we formalize FIS and make assumptions under which FIS gives an Abstract