multiplication

The passage around this formula

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 $P_r$ 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 holding a reservation that sits partly idle; above it, the…

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