Math & Numbers
Steady-state M/M/1 metrics: ρ, P0, L, Lq, W, Wq, state probabilities, and Little's-law cross-checks; unstable λ ≥ μ inputs are rejected.
Call this tool from your code in three languages.
curl -X POST 'http://127.0.0.1:3003/en/api/tools/queuing-theory-mm1' \
-H 'Content-Type: application/json' \
-d '{"arrivalRate":4,"serviceRate":6,"decimalPlaces":4}'Send a POST request with your inputs as JSON. File parameters require a separate upload first.
POST http://127.0.0.1:3003/en/api/tools/queuing-theory-mm1| Name | Type | Required | Description |
|---|---|---|---|
| arrivalRate | number | Yes | Average arrivals per time unit (Poisson process). Must be below the service rate μ. |
| serviceRate | number | Yes | Average services per time unit (exponential distribution). Must exceed the arrival rate λ. |
| decimalPlaces | number | No | — |
Text result
{
"result": "Processed text content",
"error": "Error message (optional)",
"message": "Notification message (optional)",
"metadata": {
"key": "value"
}
}Add this tool to your Model Context Protocol server so AI agents can list and call it.
Add this block to your MCP client configuration:
{
"mcpServers": {
"elysiatools-queuing-theory-mm1": {
"name": "queuing-theory-mm1",
"description": "Steady-state M/M/1 metrics: ρ, P0, L, Lq, W, Wq, state probabilities, and Little's-law cross-checks; unstable λ ≥ μ inputs are rejected.",
"baseUrl": "http://127.0.0.1:3003/mcp/sse?toolId=queuing-theory-mm1",
"command": "",
"args": [],
"env": {},
"isActive": true,
"type": "sse"
}
}
}After connecting to the SSE endpoint, list the exposed tools:
{
"jsonrpc": "2.0",
"id": 1,
"method": "tools/list"
}Invoke the tool by its id, passing arguments built from its parameters:
{
"jsonrpc": "2.0",
"id": 2,
"method": "tools/call",
"params": {
"name": "queuing-theory-mm1",
"arguments": {
"arrivalRate": 4,
"serviceRate": 6,
"decimalPlaces": 4
}
}
}Questions or issues? Contact [email protected]