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Published equation contexts

Pr<u⋅Pd,i.e.u>PrPd≡u∗P_r < u \cdot P_d, \qquad \text{i.e.} \qquad u > \frac{P_r}{P_d} \equiv u^{*}

Why this formula appears here

Here the break-even arithmetic is genuinely simple, and worth writing down, because it is the one place in this comparison where a clean model — not a ranking of vendors — is possible. Let a reserved commitment cost PrP_r per accelerator-hour, and let the on-demand or serverless rate that would otherwise serve the same throughput cost PdP_d per accelerator-hour at full utilization. If the buyer’s realized utilization of the reserved capacity is u ∈\in (0, 1] , the reserved option is cheaper exactly when Pr<u⋅Pd,i.e.u>PrPd≡u∗P_r < u \cdot P_d, \qquad \text{i.e.} \qquad u > \frac{P_r}{P_d} \equiv u^{*}. Below the break-even utilization u∗u^{*} , paying on demand only for the hours actually used is cheaper than holding a reservation that sits partly idle; above it, the…

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uu

Symbol u

u is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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PdP_d

Symbol P_d

PdP_d occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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With a fixed numerator, increasing a nonzero denominator reduces the fraction.

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

Pr<u⋅Pd,i.e.u>PrPd≡u∗.P_r < u \cdot P_d, \qquad \text{i.e.} \qquad u > \frac{P_r}{P_d} \equiv u^{*}.

Equation 10 · Inference Economics

Comparing the Main Approaches to AI Inference Economics

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

Here the break-even arithmetic is genuinely simple, and worth writing down, because it is the one place in this comparison where a clean model — not a ranking of vendors — is possible. Let a reserved commitment cost PrP_r per accelerator-hour, and let the on-demand or serverless rate that would otherwise serve the same throughput cost PdP_d per accelerator-hour at full utilization. If the buyer’s realized utilization of the reserved capacity is u ∈\in (0, 1] , the reserved option is cheaper exactly when Pr<u⋅Pd,i.e.u>PrPd≡u∗P_r < u \cdot P_d, \qquad \text{i.e.} \qquad u > \frac{P_r}{P_d} \equiv u^{*}. Below the break-even utilization u∗u^{*} , paying on demand only for the hours actually used is cheaper than holding a reservation that sits partly idle; above it, the…

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