addition

The passage around this formula

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 $c_{\mathrm{local}}$ for the cost — in latency, energy, or both — of attempting the request locally, $c_{\mathrm{cloud}}$ 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 $E[C] = c_{\mathrm{local}} + (1-p)\, c_{\mathrm{cloud}}$. The…

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