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Equation 26 · The Real Economics of Shipping a Model to a Device

What does this equation mean?

U≈Ndevices⋅Bupdate⋅pegress,U \approx N_{\mathrm{devices}} \cdot B_{\mathrm{update}} \cdot p_{\mathrm{egress}},

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This equation gives an approximation: it relates the quantities while allowing an approximation. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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UU

Symbol U

the least discussed term in this accounting and, at fleet scale, sometimes the largest.

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NdevicesN_{\mathrm{devices}}

Symbol N_devices

NdN_devices is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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BupdateB_{\mathrm{update}}

Symbol B_update

BuB_update is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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pegressp_{\mathrm{egress}}

Symbol p_egress

pep_egress is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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≈

≈

Approximately equal to; the equality is not exact.

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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

Its accuracy depends on the assumptions and range of use described in the article.

What the article says around this equation

U is the least discussed term in this accounting and, at fleet scale, sometimes the largest. It can be approximated as U≈Ndevices⋅Bupdate⋅pegressU \approx N_{\mathrm{devices}} \cdot B_{\mathrm{update}} \cdot p_{\mathrm{egress}}. the number of devices in the fleet, times the bytes pushed to each device per update, times the price per byte of moving that data. Amazon’s published CloudFront pricing states data transfer out to the internet at $0.085 per gigabyte for the first nine terabytes per month in the United States, Mexico and Canada tier, after a free first terabyte [ 14 ] . As an illustrative calculation only, using that public list price rather than any negotiated enterprise rate: a modest 200-megabyte delta update pushed to a fifty-million-device fleet is ten million…
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U is the least discussed term in this accounting and, at fleet scale, sometimes the largest. It can be approximated as U≈Ndevices⋅Bupdate⋅pegressU \approx N_{\mathrm{devices}} \cdot B_{\mathrm{update}} \cdot p_{\mathrm{egress}}. the number of devices in the fleet, times the bytes pushed to each device per update, times the price per byte of moving that data. Amazon’s published CloudFront pricing states data transfer out to the internet at $0.085 per gigabyte for the first nine terabytes per month in the United States, Mexico and Canada tier, after a free first terabyte [ 14 ] . As an illustrative calculation only, using that public list price rather than any negotiated enterprise rate: a modest 200-megabyte delta update pushed to a fifty-million-device fleet is ten million gigabytes of egress, or roughly $850,000 at that listed rate — before any volume discount, delta-patch efficiency gain, or CDN caching a real operator would negotiate. A full model re-download rather than a delta patch, at two gigabytes per device across the same fleet, would be an order of magnitude higher. Real operators pay less than this ceiling through bulk contracts and patch efficiency, but the ceiling illustrates why U belongs in the equation at all: it is a cost that scales with fleet size regardless of how many of those devices ever actually invoke the feature being updated, which is precisely the same property that makes CdevC_{\mathrm{dev}} dangerous to ignore.

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Sources cited in the surrounding passage

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