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
- 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.
- The occupancy warning — anywhere occupancy exceeds ~90%, say plainly: the SLA may hold while the team burns out; staff for the humans.
- The folklore contrast — the naive tickets-per-agent number next to the Erlang answer, so the reader sees what the old method was hiding.
- Model limits, stated — M/M/c assumes Poisson arrivals; real queues are burstier, so these are floors.
Programmatic Helper
This skill ships scripts/erlang_staffing.py — zero dependencies; run it rather than approximating:
python3 scripts/erlang_staffing.py plan staffing.xlsx --arrivals 120 --aht 6 --sla 0.8 --answer-in 60 --shrinkage 0.3
Prints the base case (base 15 on-queue / 22 rostered · SL 81% · ASA 38s · occ 80%) and writes an .xlsx with editable assumption cells and the scenario table. Requires a code-execution environment.
Quality Checks
- Numbers come from the script's Erlang C computation, quoted — never estimated in prose
- Shrinkage is applied and its value stated; a 0% shrinkage plan is flagged as fiction
- Occupancy appears next to every scenario, with the >90% burnout warning where it triggers
- Peak-hour arrivals were used, or the answer says "daily average used — peaks will breach"
- The M/M/c floor-not-ceiling caveat is present
Anti-Patterns
- Do not staff to average load — the queue's whole cruelty lives in the peaks
- Do not present on-queue count as headcount — shrinkage is the difference between a model and a roster
- Do not chase 99% SLAs without showing the cost curve — the last few points of service level are where budgets go to die
- Do not ignore occupancy because the SLA passes — attrition is a lagging indicator of this exact number
- Do not use this for email/async queues with day-long SLAs without saying the model degrades — Erlang C is built for live channels