Systems Capacity Calculators
M/M/1 and M/M/c queue: utilisation, probability of waiting (Erlang C), queue length, wait and response time, tail odds.
InferenceLiveeip155:8453Exactvia cdp
QueueingMm1MmcErlang-c
Calls · 30d
1
This endpoint's own trailing-30-day call count, as published by the upstream catalog and snapshotted daily. 4 snapshots so far.
$24.31
Verified settled volume
1,175 settlements proven x402 by their on-chain EIP-3009 marker.
$0.020
Listed price
As published in the catalog. Always read the live 402 before paying.
1
Calls · 30d
Upstream's own call count for this endpoint, not ours.
1
Unique payers · 30d
Last called 2026-10-20 20:46Z
—
Upstream on-chain volume
Reported by the source catalog.
Paid to
0xb531320805C5BED1D46AEaDcF4F008FDF172DBDaThe wallet the 402 directs payment to. Its whole payment record — every payer, every chain — is on the merchant page.
Asset 0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913
Provider
The payTo wallet does not resolve to a registered ERC-8004 agent. That is not a verdict on the service — most of the catalog is unregistered.
Live 402 challenge
Captured by the enrichment pass, not read just now. Prices can change — always read the 402 the endpoint answers with.
{
"error": "Payment required",
"accepts": [
{
"asset": "0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913",
"extra": {
"name": "USD Coin",
"version": "2"
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"payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
"scheme": "exact",
"network": "base",
"mimeType": "application/json",
"resource": "https://data-calc.x402tookit.com/queue-model",
"description": "M/M/1 and M/M/c queue: utilisation, probability of waiting (Erlang C), queue length, wait and response time, tail odds.",
"outputSchema": {
"input": {
"type": "http",
"method": "GET",
"queryParams": {
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"arrivalRate": 8,
"serviceRate": 10,
"waitThreshold": 0.5
}
},
"output": {
"asOf": "2026-10-11T20:19:39.979Z",
"model": "M/M/1",
"source": "computed locally (M/M/c queueing theory)",
"reasons": [
"Waiting time explodes as utilisation approaches 100%: for M/M/1 the mean wait is rho / (mu (1 - rho)).",
"Erlang C gives the probability that an arrival must queue; pooling servers (one queue, c servers) is much better than c separate queues.",
"…1 more"
],
"summary": "M/M/1: utilisation 80.0%, P(wait) 80.00%, mean wait 0.4000, response 0.5000 (service alone 0.1000), 3.200 waiting on average. P(wait > 0.5) = 29.43%.",
"verdict": "BUSY",
"degraded": false,
"disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
"notChecked": [
"non-Poisson arrivals and non-exponential service times (real service times with higher variance wait longer: Pollaczek-Khinchine for M/G/1)",
"limited queue capacity, abandonment and retries",
"…2 more"
],
"utilization": 0.8,
"meanInSystem": 4.000000000000002,
"meanQueueLength": 3.2000000000000015,
"meanServiceTime": 0.1,
"meanWaitInQueue": 0.4000000000000002,
"meanTimeInSystem": 0.5000000000000002,
"probabilityNoWait": 0.19999999999999996,
"offeredLoadErlangs": 0.8,
"meanWaitGivenWaiting": 0.5,
"probabilityOfWaiting": 0.8,
"probabilityEmptySystem": 0.19999999999999996,
"probabilityWaitExceedsThreshold": {
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}
},
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"description": "M/M/1 and M/M/c queue: utilisation, probability of waiting (Erlang C), queue length, wait and response time, tail odds.",
"outputSchema": {
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"output": {
"asOf": "2026-10-11T20:19:39.979Z",
"model": "M/M/1",
"source": "computed locally (M/M/c queueing theory)",
"reasons": [
"Waiting time explodes as utilisation approaches 100%: for M/M/1 the mean wait is rho / (mu (1 - rho)).",
"Erlang C gives the probability that an arrival must queue; pooling servers (one queue, c servers) is much better than c separate queues.",
"…1 more"
],
"summary": "M/M/1: utilisation 80.0%, P(wait) 80.00%, mean wait 0.4000, response 0.5000 (service alone 0.1000), 3.200 waiting on average. P(wait > 0.5) = 29.43%.",
"verdict": "BUSY",
"degraded": false,
"disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
"notChecked": [
"non-Poisson arrivals and non-exponential service times (real service times with higher variance wait longer: Pollaczek-Khinchine for M/G/1)",
"limited queue capacity, abandonment and retries",
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"utilization": 0.8,
"meanInSystem": 4.000000000000002,
"meanQueueLength": 3.2000000000000015,
"meanServiceTime": 0.1,
"meanWaitInQueue": 0.4000000000000002,
"meanTimeInSystem": 0.5000000000000002,
"probabilityNoWait": 0.19999999999999996,
"offeredLoadErlangs": 0.8,
"meanWaitGivenWaiting": 0.5,
"probabilityOfWaiting": 0.8,
"probabilityEmptySystem": 0.19999999999999996,
"probabilityWaitExceedsThreshold": {
"t": 0.5,
"probability": 0.2943035529371539
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}
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"extra": {
"name": "USD Coin",
"version": "2"
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"payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
"scheme": "exact",
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"mimeType": "application/json",
"resource": "https://data-calc.x402tookit.com/queue-model",
"description": "M/M/1 and M/M/c queue: utilisation, probability of waiting (Erlang C), queue length, wait and response time, tail odds.",
"outputSchema": {
"input": {
"type": "http",
"method": "GET",
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"serviceRate": 10,
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"output": {
"asOf": "2026-10-11T20:19:39.979Z",
"model": "M/M/1",
"source": "computed locally (M/M/c queueing theory)",
"reasons": [
"Waiting time explodes as utilisation approaches 100%: for M/M/1 the mean wait is rho / (mu (1 - rho)).",
"Erlang C gives the probability that an arrival must queue; pooling servers (one queue, c servers) is much better than c separate queues.",
"…1 more"
],
"summary": "M/M/1: utilisation 80.0%, P(wait) 80.00%, mean wait 0.4000, response 0.5000 (service alone 0.1000), 3.200 waiting on average. P(wait > 0.5) = 29.43%.",
"verdict": "BUSY",
"degraded": false,
"disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
"notChecked": [
"non-Poisson arrivals and non-exponential service times (real service times with higher variance wait longer: Pollaczek-Khinchine for M/G/1)",
"limited queue capacity, abandonment and retries",
"…2 more"
],
"utilization": 0.8,
"meanInSystem": 4.000000000000002,
"meanQueueLength": 3.2000000000000015,
"meanServiceTime": 0.1,
"meanWaitInQueue": 0.4000000000000002,
"meanTimeInSystem": 0.5000000000000002,
"probabilityNoWait": 0.19999999999999996,
"offeredLoadErlangs": 0.8,
"meanWaitGivenWaiting": 0.5,
"probabilityOfWaiting": 0.8,
"probabilityEmptySystem": 0.19999999999999996,
"probabilityWaitExceedsThreshold": {
"t": 0.5,
"probability": 0.2943035529371539
}
}
},
"maxAmountRequired": "20000",
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],
"x402Version": 1,
"alsoAvailable": {
"llms": "https://data-calc.x402tookit.com/llms.txt",
"catalog": "https://data-calc.x402tookit.com/catalog",
"message": "Systems Capacity Calculators has 10 pay-per-call endpoints (Big-O growth, RAID capacity, storage growth, latency and throughput budgets, Little's law, queueing, Erlang and SLA downtime.), from $0.02 a call. See the full menu and send your agents our way.",
"openapi": "https://data-calc.x402tookit.com/openapi.json",
"related": [
{
"url": "https://data-calc.x402tookit.com/littles-law",
"path": "/littles-law",
"what": "Little's law L = rate x time in system: solve for concurrency, throughput or latency give…",
"price": "$0.02"
},
{
"url": "https://data-calc.x402tookit.com/raid-capacity",
"path": "/raid-capacity",
"what": "RAID 0/1/5/6/10 and ZFS RAID-Z usable capacity, efficiency, fault tolerance, write penalt…",
"price": "$0.02"
},
{
"url": "https://data-calc.x402tookit.com/sla-downtime",
"path": "/sla-downtime",
"what": "SLA availability (99.9 percent, three nines) to allowed downtime per day, month and year;…",
"price": "$0.02"
}
]
}
}Accepts
The payment requirements as published to the catalog. Read the live 402 before paying — a price here is a claim, not a quote.
0.02USDC≈ $0.02 USD
on Base · exact scheme
Pay 0.02 USDC on Base to 0xb531…2DBDa. The signed payment is good for 5 minutes.
- Paid to
- 0xb531…2DBDa
- USD Coin contract
- 0x8335…02913
- Payment window
- 5 minutes
- As published
- 20000 smallest units
20000units
on solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp · exact scheme
That figure is in the token’s smallest units. Roundhouse does not hold this contract’s decimals, so it is shown as published rather than converted.
- Paid to
- DUPiup…eEm8s
- Token contract
- EPjFWd…TDt1v
- Payment window
- 5 minutes
20000units
on Polygon · exact scheme
That figure is in the token’s smallest units. Roundhouse does not hold this contract’s decimals, so it is shown as published rather than converted.
- Paid to
- 0xb531…2DBDa
- Token contract
- 0x3c49…c3359
- Payment window
- 5 minutes
20000units
on Arbitrum · exact scheme
That figure is in the token’s smallest units. Roundhouse does not hold this contract’s decimals, so it is shown as published rather than converted.
- Paid to
- 0xb531…2DBDa
- Token contract
- 0xaf88…e5831
- Payment window
- 5 minutes
The catalog’s raw entry
[
{
"asset": "0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913",
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"payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
"amount": "20000",
"scheme": "exact",
"network": "eip155:8453",
"maxTimeoutSeconds": 300
},
{
"asset": "EPjFWdd5AufqSSqeM2qN1xzybapC8G4wEGGkZwyTDt1v",
"extra": {
"feePayer": "D6ZhtNQ5nT9ZnTHUbqXZsTx5MH2rPFiBBggX4hY1WePM"
},
"payTo": "DUPiupXtuox38dcGoXUKer5mAydCzmaHjrbQ66qeEm8s",
"amount": "20000",
"scheme": "exact",
"network": "solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp",
"maxTimeoutSeconds": 300
},
{
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"extra": {
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"payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
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{
"asset": "0xaf88d065e77c8cC2239327C5EDb3A432268e5831",
"extra": {
"name": "USD Coin",
"version": "2"
},
"payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
"amount": "20000",
"scheme": "exact",
"network": "eip155:42161",
"maxTimeoutSeconds": 300
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]Extensions
{
"bazaar": {
"info": {
"input": {
"type": "http",
"method": "GET",
"queryParams": {
"servers": 1,
"arrivalRate": 8,
"serviceRate": 10,
"waitThreshold": 0.5
}
},
"output": {
"type": "json",
"example": {
"asOf": "2026-10-11T20:19:39.979Z",
"model": "M/M/1",
"source": "computed locally (M/M/c queueing theory)",
"reasons": [
"Waiting time explodes as utilisation approaches 100%: for M/M/1 the mean wait is rho / (mu (1 - rho)).",
"Erlang C gives the probability that an arrival must queue; pooling servers (one queue, c servers) is much better than c separate queues.",
"…1 more"
],
"summary": "M/M/1: utilisation 80.0%, P(wait) 80.00%, mean wait 0.4000, response 0.5000 (service alone 0.1000), 3.200 waiting on average. P(wait > 0.5) = 29.43%.",
"verdict": "BUSY",
"degraded": false,
"disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
"notChecked": [
"non-Poisson arrivals and non-exponential service times (real service times with higher variance wait longer: Pollaczek-Khinchine for M/G/1)",
"limited queue capacity, abandonment and retries",
"…2 more"
],
"utilization": 0.8,
"meanInSystem": 4.000000000000002,
"meanQueueLength": 3.2000000000000015,
"meanServiceTime": 0.1,
"meanWaitInQueue": 0.4000000000000002,
"meanTimeInSystem": 0.5000000000000002,
"probabilityNoWait": 0.19999999999999996,
"offeredLoadErlangs": 0.8,
"meanWaitGivenWaiting": 0.5,
"probabilityOfWaiting": 0.8,
"probabilityEmptySystem": 0.19999999999999996,
"probabilityWaitExceedsThreshold": {
"t": 0.5,
"probability": 0.2943035529371539
}
}
}
},
"schema": {
"type": "object",
"$schema": "https://json-schema.org/draft/2020-12/schema",
"required": [
"input"
],
"properties": {
"input": {
"type": "object",
"required": [
"type",
"method"
],
"properties": {
"type": {
"type": "string",
"const": "http"
},
"method": {
"enum": [
"GET"
],
"type": "string"
},
"queryParams": {
"type": "object",
"required": [
"arrivalRate",
"serviceRate"
],
"properties": {
"servers": {
"type": "integer",
"description": "Number of servers c (default 1 = M/M/1), 1 to 1000"
},
"arrivalRate": {
"type": "number",
"description": "Arrival rate lambda per time unit (e.g. per second)"
},
"serviceRate": {
"type": "number",
"description": "Service rate mu of ONE server per the same time unit (1 / mean service time)"
},
"waitThreshold": {
"type": "number",
"description": "Optional time t (same unit as the rates inverse): returns P(wait in queue > t)"
}
}
}
},
"additionalProperties": false
},
"output": {
"type": "object",
"required": [
"type"
],
"properties": {
"type": {
"type": "string"
},
"example": {
"type": "object",
"properties": {
"asOf": {
"type": [
"null",
"string"
]
},
"model": {
"type": [
"null",
"string"
]
},
"source": {
"type": [
"null",
"string"
]
},
"reasons": {
"type": [
"array",
"null"
],
"items": {
"type": "string"
}
},
"summary": {
"type": [
"null",
"string"
]
},
"verdict": {
"type": [
"null",
"string"
]
},
"degraded": {
"type": [
"boolean",
"null"
]
},
"disclaimer": {
"type": [
"null",
"string"
]
},
"notChecked": {
"type": [
"array",
"null"
],
"items": {
"type": "string"
}
},
"utilization": {
"type": [
"null",
"number"
]
},
"meanInSystem": {
"type": [
"null",
"number"
]
},
"meanQueueLength": {
"type": [
"null",
"number"
]
},
"meanServiceTime": {
"type": [
"null",
"number"
]
},
"meanWaitInQueue": {
"type": [
"null",
"number"
]
},
"meanTimeInSystem": {
"type": [
"null",
"number"
]
},
"probabilityNoWait": {
"type": [
"null",
"number"
]
},
"offeredLoadErlangs": {
"type": [
"null",
"number"
]
},
"meanWaitGivenWaiting": {
"type": [
"null",
"number"
]
},
"probabilityOfWaiting": {
"type": [
"null",
"number"
]
},
"probabilityEmptySystem": {
"type": [
"null",
"number"
]
},
"probabilityWaitExceedsThreshold": {
"type": [
"null",
"object"
],
"properties": {
"t": {
"type": [
"null",
"number"
]
},
"probability": {
"type": [
"null",
"number"
]
}
}
}
}
}
}
}
}
}
}
}Provenance
- Seen in the source catalog
- 2026-10-20 20:46Z
- Last indexed by Roundhouse
- 2026-10-22 06:50Z
- Last enriched (probe, favicon, geo)
- 2026-10-20 23:45Z
- x402 version
- 2
- Max timeout
- 300s
- Liveness probe
- HTTP 402
Hand this page to an agent
Copy the prompt and paste it into Claude, an MCP client or your own agent — it will vet this service and call it over the free read API. No key, no account.
GET api.roundhouseai.io/v0/endpoints
This endpoint's own trailing-30-day call count, as published by the upstream catalog and snapshotted daily. 4 snapshots so far. Verified volume counts only settlements with an on-chain EIP-3009 marker.
Show the promptHide the prompt
Using Roundhouse, look up the x402 service Systems Capacity Calculators and tell me whether it is worth paying: what a call costs, whether the endpoint answered when last probed, and what its payment record actually shows. curl -s 'https://api.roundhouseai.io/v0/endpoints?q=Systems%20Capacity%20Calculators' curl -s 'https://api.roundhouseai.io/v0/merchants/<the payTo wallet returned above>' Then call it: read the price from the live 402 at https://data-calc.x402tookit.com/queue-model, never from a cached figure, and pay with an x402 client. The /v0 API needs an API key (`authorization: Bearer rh_live_…`) on everything except /v0/unified* and /v0/endpoints. Either pay over x402 (mint a personal key for $0.01 at GET https://api.roundhouseai.io/v0/test/x402), or ask me for an organization key, which I create at https://roundhouseai.io/dashboard/connections. If you have neither, ask before going further. If you do not have Roundhouse tools or skills installed, read https://roundhouseai.io/skill.md first — it is the whole procedure.