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Equation 1 · Part 8 · AI Accelerator Architecture in Practice: An Advanced Technical Guide

subscript

Tfleet=N⋅Pdevice⋅Usustained⋅A,T_{\mathrm{fleet}} = N \cdot P_{\mathrm{device}} \cdot U_{\mathrm{sustained}} \cdot A,
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

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 Tfleet=N⋅Pdevice⋅Usustained⋅AT_{\mathrm{fleet}} = N \cdot P_{\mathrm{device}} \cdot U_{\mathrm{sustained}} \cdot A. where N is the device count, PdeviceP_{\mathrm{device}} is a single device’s measured (not advertised) throughput on the actual workload, UsustainedU_{\mathrm{sustained}} is the utilization fraction observed over a representative…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

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