Optimal age-dependent checkpoint strategy with retry of rollback recovery

We consider a file system with age-dependent checkpointing, where the rollback recovery operation after a system failure may be imperfect with positive unsuccessful probability. After a few mathematical preliminaries, we formulate the steady-state availability and obtain the age-dependent checkpoint strategy analytically, maximizing the steady-state availability. In a numerical example, we examine the dependence of the unsuccessful probability of rollback recovery on the optimal checkpoint interval, and refer to the effect of imperfect rollback recovery quantitatively.