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

What does this equation mean?

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

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Inputs and operationsN × P_device × U_sustained × A
Result or conditionT_fleet
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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TfleetT_{\mathrm{fleet}}

Symbol T_fleet

the simple way to state the assumption explicitly.

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NN

Symbol N

N is one factor in the product that computes the quantity on the left.

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PdeviceP_{\mathrm{device}}

Symbol P_device

a single device’s measured (not advertised) throughput on the actual workload.

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UsustainedU_{\mathrm{sustained}}

Symbol U_sustained

the utilization fraction observed over a representative multi-hour or multi-day window rather than a benchmark’s best run.

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AA

Symbol 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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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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multiplication

multiplication

Multiply the quantities on either side.

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subscript

subscript

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.

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How to interpret it

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What the article says around this equation

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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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 multi-hour or multi-day window rather than a benchmark’s best run, and A is availability — the fraction of time the fleet is actually up and assigned to the job rather than down for failure, repair, or checkpoint recovery. Treating A as 1 is the single most common capacity-planning error, and it is the one large-scale operators are most explicit about correcting for.

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