Equation 10 · Part 4 · Comparing the Main Approaches to AI Inference Economics

Symbol u^*

P_r < u \cdot P_d, \qquad \text{i.e.} \qquad u > \frac{P_r}{P_d} \equiv u^{*}.

u^{*}

What this part means

the below the break-even utilization.

Its job in the formula

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

Full expressionSymbol u^*Article meaning

Where the article explains it

Below the break-even utilization $u^{*}$ , paying on demand only for the hours actually used is cheaper than holding a reservation that sits partly idle; above it, the reservation wins.

The passage around this formula

…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 $P_r < u \cdot P_d, \qquad \text{i.e.} \qquad u > \frac{P_r}{P_d} \equiv u^{*}$ . Below the break-even utilization $u^{*}$ , paying on demand only for the hours actually used is cheaper than holding a reservation that sits partly idle; above it, the reservation wins. What no published rate card can supply is u itself — a property of the buyer’s own traffic, not of any vendor’s pricing page — which is exactly why…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

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