Equation 10 · Part 3 · Comparing the Main Approaches to AI Inference Economics

Symbol P_d

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

P_d

What this part means

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

Its job in the formula

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

Full expressionSymbol P_dArticle meaning

The passage around this formula

…where a clean model — not a ranking of vendors — is possible. Let a reserved commitment cost $P_r$ per accelerator-hour, and let the on-demand or serverless rate that would otherwise serve the same throughput cost $P_d$ 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 $P_r < u \cdot P_d, \qquad \text{i.e.} \qquad u > \frac{P_r}{P_d} \equiv u^{*}$ . Below the break-even utilization $u^{*}$ , paying on demand only for the hours actually used is cheaper than…

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