add pool sizing calculator to reserved browsers overview

[dprevoznik]

Summary

• New interactive calculator at the bottom of browsers/pools/overview.mdx that recommends a reserved pool size from acquisition rate, average acquired duration, and fill rate.
• Calculator assumes reuse: false on release (every acquisition triggers a refill). It computes both the concurrency floor (Little's Law with a 1.25× safety factor to match the FAQ's 10–20% headroom guidance) and the refill floor (driven by the 25%-per-minute fill ceiling), and returns the larger of the two with a "binding constraint" indicator.
• Docs section explains the equation, the ~3.2-minute crossover between the two constraints, and a small worked-examples table.

Formula

concurrency_floor = ceil(λ × d × 1.25)
refill_floor      = ceil(100 × λ / fill_rate)
N                 = max(concurrency_floor, refill_floor)

Test plan

• Mintlify preview renders the calculator inside the overview page
• Inputs update the recommended size live and flash on change
• Fill rate clamps to 1–25
• Worked-examples table values match the calculator output
• URL query params (acquisitionRate, sessionDuration, fillRate) update on interaction, matching the existing pricing calculator pattern

[mintlify]

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Project	Status	Preview	Updated (UTC)
Kernel	🟢 Ready	View Preview	Jun 2, 2026, 3:29 PM

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[cursor]

Risk assessment: Low risk.

Evidence from the diff: this PR modifies browsers/pools/overview.mdx and adds an isolated snippets/pool-sizing-calculator.jsx Mintlify snippet for a docs-page calculator. The change is user-facing documentation UI, but it doesn't modify production runtime code, auth, permissions, billing, infrastructure, shared libraries, or data/schema behavior. I also found no CODEOWNERS file in the repo and no existing approvals on the PR, so approval is appropriate under the requested rules.

  

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[cursor]

Risk assessment: Low risk.

Evidence from the diff: this PR modifies browsers/pools/overview.mdx and adds snippets/pool-sizing-calculator.jsx, an isolated Mintlify docs-page calculator. The change is user-facing documentation UI, but it doesn't touch production application code, auth, permissions, billing, infrastructure, shared libraries, data/schema behavior, or deployment configuration. The snippet only performs local calculator state updates and URL query/hash replacement in the browser.

I found no CODEOWNERS file in the repo. The PR is already approved on the current head commit, so I did not add another approval.

  

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