subscript

The passage around this formula

The underlying trade-off is a classical one from checkpoint/restart theory, and it is worth making explicit because it is the model every specific policy below is an instance of. If a checkpoint costs a fixed time C to write and failures arrive with mean time between them M , then choosing a checkpoint interval T trades two costs against each other: writing more often burns time on overhead, and writing less often burns time re-doing work lost since the last save. Minimising the sum of those two costs — checkpoint overhead C/T plus expected rework T/2M — over T gives the classical optimum: $T_{\text{opt}} \approx \sqrt{2\,C\,M}$. The consequence that matters operationally is that $T_{\text{opt}}$ shrinks as M…

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