M/M/1 and M/M/c queue
M/M/1 and M/M/c queue: utilisation, probability of waiting (Erlang C), queue length, wait and response time, tail odds.
Answeringour last check, 2026-10-21
1 of 1checks answered this week
948 msmedian answer time
$0.02listed price per call
$0.02price it asked us
Paid test badge: not yet. The checks above are free: we call the tool without paying and read the payment request it sends back. The Verified badge needs paid calls whose answers match the promised output, and nobody can buy a badge.
Endpoint
GET https://data-calc.x402tookit.com/queue-model
| Category | Everything else |
|---|---|
| Provider host | data-calc.x402tookit.com |
| Networks | eip155:137, eip155:42161, eip155:8453, solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp |
| Payment schemes | exact |
| Self-reported calls, 30 days | 1 from 1 payers (the provider's figure, not ours) |
Our checks, last 30 days
| Day | Result | HTTP | Asked | Time |
|---|---|---|---|---|
| 2026-10-21 | valid payment request | 402 | $0.02 | 948 ms |
Example input (from the provider)
{
"method": "GET",
"queryParams": {
"arrivalRate": 8,
"servers": 1,
"serviceRate": 10,
"waitThreshold": 0.5
},
"type": "http"
}
Promised output schema (from the provider)
{
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"input": {
"additionalProperties": false,
"properties": {
"method": {
"enum": [
"GET"
],
"type": "string"
},
"queryParams": {
"properties": {
"arrivalRate": {
"description": "Arrival rate lambda per time unit (e.g. per second)",
"type": "number"
},
"servers": {
"description": "Number of servers c (default 1 = M/M/1), 1 to 1000",
"type": "integer"
},
"serviceRate": {
"description": "Service rate mu of ONE server per the same time unit (1 / mean service time)",
"type": "number"
},
"waitThreshold": {
"description": "Optional time t (same unit as the rates inverse): returns P(wait in queue > t)",
"type": "number"
}
},
"required": [
"arrivalRate",
"serviceRate"
],
"type": "object"
},
"type": {
"const": "http",
"type": "string"
}
},
"required": [
"type",
"method"
],
"type": "object"
},
"output": {
"properties": {
"example": {
"properties": {
"asOf": {
"type": [
"null",
"string"
]
},
"degraded": {
"type": [
"boolean",
"null"
]
},
"disclaimer": {
"type": [
"null",
"string"
]
},
"meanInSystem": {
"type": [
"null",
"number"
]
},
"meanQueueLength": {
"type": [
"null",
"number"
]
},
"meanServiceTime": {
"type": [
"null",
"number"
]
},
"meanTimeInSystem": {
"type": [
"null",
"number"
]
},
"meanWaitGivenWaiting": {
"type": [
"null",
"number"
]
},
"meanWaitInQueue": {
"type": [
"null",
"number"
]
},
"model": {
"type": [
"null",
"string"
]
},
"notChecked": {
"items": {
"type": "string"
},
"type": [
"array",
"null"
]
},
"offeredLoadErlangs": {
"type": [
"null",
"number"
]
},
"probabilityEmptySystem": {
"type": [
"null",
"number"
]
},
"probabilityNoWait": {
"type": [
"null",
"number"
]
},
"probabilityOfWaiting": {
"type": [
"null",
"number"
]
},
"probabilityWaitExceedsThreshold": {
"properties": {
"probability": {
"type": [
"null",
"number"
]
},
"t": {
"type": [
"null",
"number"
]
}
},
"type": [
"null",
"object"
]
},
"reasons": {
"items": {
"type": "string"
},
"type": [
"array",
"null"
]
},
"source": {
"type": [
"null",
"string"
]
},
"summary": {
"type": [
"null",
"string"
]
},
"utilization": {
"type": [
"null",
"number"
]
},
"verdict": {
"type": [
"null",
"string"
]
}
},
"type": "object"
},
"type": {
"type": "string"
}
},
"required": [
"type"
],
"type": "object"
}
},
"required": [
"input"
],
"type": "object"
}