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.
3. The folklore contrast — the naive tickets-per-agent number next to the Erlang answer, so the reader sees what the old method was hiding.
4. Model limits, stated — M/M/c assumes Poisson arrivals; real queues are burstier, so these are floors.

Programmatic Helper