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.
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Use support-staffing-model to In a code-execution environment, calculate Erlang C staffing scenarios and produce an editable .xlsx for [peak contacts per hour and average handle time], [SLA target], and [shrinkage percentage].
Required inputs
[peak contacts per hour and average handle time]
[SLA target]
[shrinkage percentage]
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SKILL.md
name: support-staffing-modeldescription: "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."
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
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:
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
Example Trigger Phrases
"Staffing a support/CS team."
"Defend headcount."
"Check whether an SLA is mathematically possible with the current roster."