Guarded Repair of Dependable Systems

Abstract Imperfect coverage and nonnegligible reconfiguration delay are known to have a deleterious effect on the dependability and the performance of a multiprocessor system. In particular, increasing the number of processor elements does not always increase dependability. An obvious reason for this is that the total failure rate increases, generally, linearly with the number of components in the system. It is also a well-known fact that the performance gain due to parallelism mostly turns out to be sublinear with the number of processors. It is therefore important to optimize the degree of parallelism in system design. A related issue is that by deferring repair, it is sometimes possible to improve system dependability. In this case decisions have to be made dynamically as to when to repair and when not to repair. Most of the current research deals with static optimization of the number of processors. No systematic approach for dynamic control of dependable systems has been proposed so far. Dynamic, i.e. transient, decision of whether or not to repair is the optimization problem considered in this paper. We propose extended Markov reward models (EMRM) to capture such questions. EMRM are a marriage between performability modeling techniques and Markov decision theory. A numerical solution procedure is developed to provide optimal solution trajectories for this problem. EMRM are a general framework for the dynamic optimization of reconfigurable, dependable systems. The optimization is applied on the basis of several performance and dependability measures. In particular, we explore availability, capacity-oriented availability, performance-oriented unavailability, and performability measures. Furthermore, off-line and on-line repair strategies are compared. We show that guarded repair can improve system performance and dependability significantly. The control strategies and reward functions differ a lot in each case. Each scenario turns out to be interest in its own right. A time-dependent optimality of dependable, parallel configurations can be determined from our results.