System load normally exhibits a cyclic pattern with a slack period at night and a heavy load at day [23]. Such a cyclic pattern of system load has a significant performance impact on checkpoint establishment: a heavily loaded system is likely to increase the elapsed time for a checkpoint establishment while a lightly loaded system is likely to reduce the elapsed time for a checkpoint establishment. However, the effect of the time-dependent checkpoint establishment on the optimum checkpoint placement is generally overlooked in literature. In this paper, with emphasis on the time-dependent checkpoint establishment, we develop a time-dependent approach in formulating a more realistic model and derive a close-form formula to determine the optimum checkpoint frequency. As a result, the obtained results allow for the time-varying checkpoint establishment, as well as time-varying failure rate, thereby rendering a great deal of realism to the mathematical formulation. To quantitatively evaluate the effect of time-varying checkpoint establishment, we present an example to show that in the case of time-varying check-point establishment, the optimum checkpoint placement is required to be unequally spaced even under Poisson system failures (constant failure rates).
