Optimize queue staffing SLA

What it's for

Finds the cheapest staffing level that still meets a wait-time target, across weighted demand scenarios rather than one assumed load.

Turns incident and support demand into an explainable staffing decision with stability, utilization, SLA probability, and breach economics.

What you give it

Inputs split into evidence read from your connected systems, calibration your team owns, and numerical controls that affect precision but never the result's meaning.

{
  "breach_cost_per_event": 200,
  "demand_scenarios": [
    {
      "arrival_rate_per_hour": 4,
      "id": "normal",
      "mean_service_minutes": 15,
      "probability": 0.8
    },
    {
      "arrival_rate_per_hour": 10,
      "id": "surge",
      "mean_service_minutes": 15,
      "probability": 0.2
    }
  ],
  "maximum_servers": 12,
  "required_scenario_coverage": 1,
  "server_cost_per_hour": 50,
  "sla_wait_minutes": 15,
  "target_probability_within_sla": 0.9
}

What you get back

This is the actual output of running the example above — computed by the same function the platform calls, not an illustration.

{
  "assumptions": [
    "Each scenario is a stationary M/M/c queue with Poisson arrivals, exponential service, identical parallel responders, and no abandonment.",
    "Scenario probabilities represent the planning-period demand mixture and sum to one.",
    "Breach cost is the marginal expected cost per event missing the wait-time SLA, in the same hourly units as staffing cost.",
    "Use the delivery digital twin when arrivals, service, routing, priorities, or rework materially violate Erlang-C assumptions."
  ],
  "constraints": {
    "maximum_servers": 12,
    "required_scenario_coverage": 1,
    "sla_wait_minutes": 15,
    "target_probability_within_sla": 0.9
  },
  "decision": "staffing_plan_found",
  "evaluated_staffing_levels": 12,
  "maximum_server_diagnostic": null,
  "method": "scenario_weighted_erlang_c_staffing_v1",
  "minimum_staffing_meeting_sla": 4,
  "recommended_staffing": {
    "expected_breach_cost_per_hour": 29.2,
    "expected_probability_within_sla": 0.9849,
    "expected_total_cost_per_hour": 229.2,
    "scenario_probability_meeting_target": 1,
    "scenarios": [
      {
        "expected_breaches_per_hour": 0.0041,
        "probability_within_sla": 0.999,
        "scenario_id": "normal",
        "stable": true,
        "utilization": 0.25
      },
      {
        "expected_breaches_per_hour": 0.7137,
        "probability_within_sla": 0.9286,
        "scenario_id": "surge",
        "stable": true,
        "utilization": 0.625
      }
    ],
    "servers": 4,
    "staffing_cost_per_hour": 200
  }
}

How it works

Constrained optimization — Pick the best feasible option under real limits — budget, headcount, dependencies, capacity — rather than ranking a list and hoping it fits.

1. 1 Invert an Erlang-C queue across weighted demand scenarios to find the lowest expected-cost staffing level that satisfies a wait-time SLA.
2. 2 Evaluate the method-specific diagnostics and gates returned by the function, then abstain unless the declared decision clears them under locally governed thresholds.

Before you trust it

Every tool in the catalog ships with the conditions under which its answer is meaningful — and the conditions under which it should abstain instead of guessing.

Calibrating it to your org

Calibration workflow

1. 1 Define the management decision, target outcome, aggregate unit, privacy boundary, cadence, and prediction/intervention horizon for this organization.
2. 2 Build a tenant-scoped historical cohort using only information available before each prediction or decision; preserve zero periods, censoring, assignment probabilities, and unresolved outcomes when the method requires them.
3. 3 Estimate statistical parameters on training history, but obtain costs, utilities, risk tolerance, practical-effect thresholds, capacity, and policy constraints from accountable decision owners.
4. 4 Validate on later time windows or held-out aggregate units at the deployment grain, against a simple baseline and the function-specific validation strategy.
5. 5 Deploy only if the returned decision clears evidence, overlap, calibration, robustness, and guardrail checks; warning, unsupported, schema-gap, and fallback decisions are abstentions.
6. 6 Monitor realized outcomes, data drift, coverage, and decision regret; recalibrate at a governed cadence or after a detected regime/definition change, never merely because a stakeholder dislikes the result.

Call it from your AI

You don't wire up 388 tools in your MCP client. The GitRevio MCP server exposes 18 tools, three of which let an agent search the catalog, read a tool's schema, and run it — so the assistant finds this one on its own.

gitrevio_capabilities_search
  { "q": "invert an erlangc queue across weighted" }
  → finds "optimize_queue_staffing_sla"

gitrevio_capability_describe
  { "capability_id": "optimize_queue_staffing_sla" }
  → returns the input schema and agent guidance shown on this page

gitrevio_capability_run
  { "capability_id": "optimize_queue_staffing_sla", "arguments": { ... } }
  → returns the result shown above

Works in Claude Desktop, Claude Code, Cursor, Cline, Continue.dev, Goose and Aider. See the MCP server.

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