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support-staffing-model

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How many support agents does the queue actually need — Erlang C, computed, not 'tickets per agent' folklore. Use when staffing a support/CS team, defending headcount, or checking whether an SLA is mathematically possible with the current roster. Produces agent counts across load scenarios (with shrinkage), occupancy and average-wait numbers, and a real .xlsx — via the bundled zero-dependency script.

skills/support-staffing-model/SKILL.md

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# Support Staffing Model

Queues are counterintuitive: at high occupancy, one extra contact per hour explodes wait times, and "tickets ÷ tickets-per-agent" staffing walks teams straight into the cliff. Erlang C is the century-old math call centers run on; this skill runs it for you, honestly labelled.

## Required Inputs

- **Contacts per hour** (peak hour, not daily average — queues die at peaks) and **average handle time** in minutes.
- **The SLA** — "X% answered within Y seconds/minutes". If none exists, propose one before staffing to it.
- **Shrinkage** — the fraction of paid time agents aren't available (meetings, breaks, training). Teams that skip this understaff by 30-40%; default 0.3.

## Output Format

1. **The staffing table** — for load scenarios (0.8×, 1×, 1.25×, 1.5×): agents on-queue, rostered headcount after shrinkage, achieved service level, average speed of answer, occupancy.
2. **The occupancy warning** — anywhere occupancy exceeds ~90%, say plainly: the SLA may hold while the team burns out; staff for the humans.
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