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Published equation contexts

E[C]=clocal+(1−p) ccloudE[C] = c_{\mathrm{local}} + (1-p)\, c_{\mathrm{cloud}}

Why this formula appears here

That example is useful precisely because it exposes what a “local-agent-with-fallback” architecture actually costs, which is easy to gloss over in a design review. Escalation is additive, not a substitution: a request that ultimately needs the cloud still pays for the local attempt first. Write clocalc_{\mathrm{local}} for the cost — in latency, energy, or both — of attempting the request locally, ccloudc_{\mathrm{cloud}} for the marginal cost of the network round trip once escalation is triggered, and p for the probability a request is judged solvable without escalating. If the local attempt always runs before the decision to escalate is made, the expected cost per request is E[C]=clocal+(1−p) ccloudE[C] = c_{\mathrm{local}} + (1-p)\, c_{\mathrm{cloud}}. The…

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ccloudc_{\mathrm{cloud}}

Symbol c_cloud

ccc_cloud is one of the signed contributions combined to compute the quantity on the left.

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E[C]=clocal+(1−p) ccloud.E[C] = c_{\mathrm{local}} + (1-p)\, c_{\mathrm{cloud}}.

Equation 4 · Edge AI & Electronics

Shipping an On-Device AI Feature That Actually Works in the Field

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

That example is useful precisely because it exposes what a “local-agent-with-fallback” architecture actually costs, which is easy to gloss over in a design review. Escalation is additive, not a substitution: a request that ultimately needs the cloud still pays for the local attempt first. Write clocalc_{\mathrm{local}} for the cost — in latency, energy, or both — of attempting the request locally, ccloudc_{\mathrm{cloud}} for the marginal cost of the network round trip once escalation is triggered, and p for the probability a request is judged solvable without escalating. If the local attempt always runs before the decision to escalate is made, the expected cost per request is E[C]=clocal+(1−p) ccloudE[C] = c_{\mathrm{local}} + (1-p)\, c_{\mathrm{cloud}}. The…

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