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Erlang C / M/M/c Queuing Theory Calculator
x402
Erlang C / M/M/c Queuing Theory Calculator is a paid API for AI agents from compute.siliq.io, paid per call via x402, $0.01/call, status down (last checked 2026-09-15).
Computes Erlang C wait probability, service level, and staffing recommendations for M/M/c queuing models given arrival rate, service rate, and number of agents.
Price / call$0.01
Success—
StatusDown
Output
Returns Erlang C wait probability (probability a caller must wait), achieved service level percentage, recommended number of agents to meet a target service level, queue utilization, and estimated average wait time for the given M/M/c parameters.
Example use cases
Example prompt
“We get about 150 calls per hour, each taking an average of 4 minutes to handle — can you run an Erlang C calculation to tell me how many agents we need to hit an 80% service level within 20 seconds, and what the wait probability would be at that staffing level?”
Technical details
Endpoint
POSThttps://compute.siliq.io/analytics/erlangWhen to prefer
Choose this endpoint when you need rigorous Erlang C / M/M/c queuing theory calculations for contact center staffing, support queue sizing, or any multi-server queue analysis. Prefer over general statistics or simulation APIs when you specifically need closed-form Erlang C metrics including wait probability and service level. Ideal for workforce management automation, real-time staffing adjustments, or SLA planning.
Side effects
- Invalid or negative arrival/service rate returns 400 validation error
- Agent count of zero or utilization >= 1.0 (overloaded system) returns error indicating infinite queue
- Missing required parameters returns 422 unprocessable entity
- Payment failure or insufficient USDC balance returns 402 payment required
- Extremely high traffic intensity may return numerical instability warning
Input
{
"input": {
"body": {
"num_servers": 12,
"arrival_rate": 150,
"service_rate": 15
},
"type": "http",
"method": "POST",
"bodyType": "json"
}
}Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Output
{
"prob_wait": 0.4494,
"utilization": 0.8333,
"service_level": 0.9998,
"system_stable": true,
"interpretation": "Moderate load — 83% utilization. Consider adding servers before peak demand.",
"compute_time_ms": 0,
"avg_queue_length": 2.247,
"avg_wait_time_hours": 0.015,
"recommended_servers": 11,
"avg_system_time_hours": 0.0816,
"recommended_servers_utilization": 0.9091
}Tags
x402
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