Optimal Checkpoint Interval with Availability as an Objective Function

We present a simplified derivation of the optimal checkpoint interval in Young_1974 [1]. The optimal checkpoint interval derivation in [1] is based on minimizing the total lost time as an objective-function. Lost time is a function of checkpoint interval, checkpoint save time, and average failure time. This simplified derivation yields lost-time-optimal that is identical to the one derived in [1]. For large scale-out super-computer or datacenter systems, what is important is the selection of optimal checkpoint interval that maximizes availability. We show that availability-optimal checkpoint interval is different from the one derived in [1]. However, availability-optimal checkpoint interval is asymptotically same as lost-time-optimal checkpoint interval for certain conditions on checkpoint save and recovery time. We show that these optimal checkpoint intervals hold in situations where the error detection latency is significantly smaller than any selected checkpoint interval. However, in cases where the error detection latency is very large then the optimal checkpoint interval is greater than or equal to the error detection latency.