Symbol M

The passage around this formula

with $\delta$ the time cost of writing one checkpoint and M the mean time between failures — and the paper notes that its simplified derivation reproduces the same interval as the original 1974 analysis it revisits [ 15 ] . The relationship exposes the exact trade-off cluster engineers have faced at every scale since: a checkpoint that is slow to write has to be taken less often, which increases the average work lost per failure, while a fleet whose components fail more frequently needs checkpoints taken more often regardless of how expensive each one is. As M shrank with fleet size, $\delta$ had to shrink to match, or lost work would grow without bound.

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