# Erlang C / M/M/c Queuing Theory Calculator

> 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.

## Facts

- Endpoint: POST https://compute.siliq.io/analytics/erlang
- Price: $0.01/call
- Payment: x402
- Status: down
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/compute-siliq-io-73b90732
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_BUUHFhQep7kGFush0gMVE

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability compute-siliq-io-73b90732 -d '<json body>'
```

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?

## When to prefer this

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.

## Known failure modes

- 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

## 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 request

```json
{
 "input": {
  "body": {
   "num_servers": 12,
   "arrival_rate": 150,
   "service_rate": 15
  },
  "type": "http",
  "method": "POST",
  "bodyType": "json"
 }
}
```

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method",
    "bodyType",
    "body"
   ],
   "properties": {
    "body": {
     "properties": {}
    },
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "POST",
      "PUT",
      "PATCH"
     ],
     "type": "string"
    },
    "bodyType": {
     "enum": [
      "json",
      "form-data",
      "text"
     ],
     "type": "string"
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object"
    }
   }
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/compute-siliq-io-73b90732/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from compute.siliq.io](https://www.zero.xyz/host/compute.siliq.io/llms.txt)