How Robust is the Optimal Software Rejuvenation Timing?

Robustness is usually relevant for characterizing the dependence between the values of model parameters and system behavior, and can be understood as stability of system behavior under changes in model parameters. In this paper, we consider a simple software rejuvenation model and its optimal rejuvenation timing, which maximizes the steady-state availability of the system. The main contribution of this work is to provide a new perspective on the optimal software rejuvenation timing, that is, the robustness of the optimal rejuvenation timing against input factors. In particular, the degree of robustness is quantified by the first derivatives of the optimal rejuvenation timing with respect to the model parameters. The robustnesses of both optimal rejuvenation timing and system availability with the optimal rejuvenation timing are considered. A numerical example with Weibull distributed failure time is devoted to clarifying how robust the optimal rejuvenation timing is, and determine the most sensitive model parameter. As a result, the optimal rejuvenation timing seems to be more robust to the parameters regarding failure time distribution, compared with the other parameters.