$$T_{\mathrm{fleet}} = N \cdot P_{\mathrm{device}} \cdot U_{\mathrm{sustained}} \cdot A$$

Equation 1 · Semiconductors

AI Accelerator Architecture in Practice: An Advanced Technical Guide

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Capacity planning built on a vendor’s peak specification, or even on a single well-tuned benchmark run, systematically overestimates what a production fleet delivers, because it leaves out two things that only show up at sustained, continuous operation: the utilization gap already discussed, and the fraction of wall-clock time the fleet is not running at all. A workable capacity model has to account for both. A simple way to state the assumption explicitly is $T_{\mathrm{fleet}} = N \cdot P_{\mathrm{device}} \cdot U_{\mathrm{sustained}} \cdot A$. where N is the device count, $P_{\mathrm{device}}$ is a single device’s measured (not advertised) throughput on the actual workload, $U_{\mathrm{sustained}}$ is the utilization fraction observed over a representative…

Meanings in this article

• $T_{\mathrm{fleet}}$: the simple way to state the assumption explicitly.
• $P_{\mathrm{device}}$: a single device’s measured (not advertised) throughput on the actual workload.
• $U_{\mathrm{sustained}}$: the utilization fraction observed over a representative multi-hour or multi-day window rather than a benchmark’s best run.
• $A$: availability — the fraction of time the fleet is actually up and assigned to the job rather than down for failure, repair, or checkpoint recovery.

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