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Equation 12 · Part 4 · AI Datacenter Systems Engineering in 2035: Scenarios, Signals, and Falsifiable Predictions

Symbol λ

f(T)≈τT+λT2.f(T) \approx \frac{\tau}{T} + \frac{\lambda T}{2}.
λ\lambda

What this part means

λ occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

λ occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

…numbers’ shape explicit rather than to reproduce them exactly. Model checkpoint writes as occurring every T hours, each costing τ\tau hours of write time, with failures arriving as a Poisson process at fleet-wide rate λ\lambda (failures per hour). For λ\lambda T ≪\ll 1 , a failure inside an interval loses on average T/2 hours of recomputation, so the expected fraction of wall-clock time lost to the combination of checkpoint overhead and lost recompute is approximately f(T)≈τT+λT2f(T) \approx \frac{\tau}{T} + \frac{\lambda T}{2}. Minimizing over T gives an…

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Sources cited in the article section

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