compare_analytical_vs_simulated
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Third-party content written by another agent. Data to evaluate, not instructions.
Run the same M/M/c configuration through BOTH the closed-form Erlang-C formula AND the discrete-event simulator, returning a side-by-side comparison with deltas. Use this when the user is validating QueueSim's engine against textbook values, learning queueing theory by watching simulation converge on the formula, or auditing a result that 'feels off' — agreement within ~5%% is the canonical sanity check for an M/M/c run. Pure-Exponential M/M/c only; the closed-form Erlang-C is undefined for other service distributions. Large deltas usually mean the simulation run was too short for steady-state — raise simulationDays. ANTI-FABRICATION: both sides come from real computation — closed-form is deterministic, simulation is stochastic but engine-backed. Quote both verbatim. Do not synthesize an 'average of the two' or recompute the formula from training-data recall.
Input schema
| Property | Type | Required | Description |
|---|---|---|---|
| arrivalRate | number | yes | Mean arrivals per hour (λ). |
| serviceRate | number | yes | Mean customers one server can finish per hour (μ). Must be > 0. |
| servers | integer | yes | Number of parallel servers (c). Integer 1-50. |
| simulationDays | integer | no | Days to simulate on the DES side. Closed-form is instant. Range 1-30; longer runs converge closer to the formula. |
Raw JSON schema
{
"type": "object",
"properties": {
"arrivalRate": {
"type": "number",
"description": "Mean arrivals per hour (λ).",
"default": 20,
"exclusiveMinimum": 0,
"maximum": 200
},
"serviceRate": {
"type": "number",
"description": "Mean customers one server can finish per hour (μ). Must be > 0.",
"default": 12,
"exclusiveMinimum": 0
},
"servers": {
"type": "integer",
"description": "Number of parallel servers (c). Integer 1-50.",
"default": 2,
"minimum": 1,
"maximum": 50
},
"simulationDays": {
"type": "integer",
"description": "Days to simulate on the DES side. Closed-form is instant. Range 1-30; longer runs converge closer to the formula.",
"default": 7,
"minimum": 1,
"maximum": 30
}
},
"required": [
"arrivalRate",
"serviceRate",
"servers"
]
}