← The evidence ledger
Evidence row 2202005
Observed , by sync.x402_bazaar/1.
- Kind
- listing
- About
- source_record x402_bazaar:https://data-calc.x402tookit.com/queue-model
- Recorded
- Previous row
- None: the first of its kind about this subject
- Body SHA-256
- 6f015fbfb19510fe1f55b12c1d547ff24aa6d8d91dac930746960aa3db58a0be
- Leaf
- 0x1225a5791c1609e7d6a5beecca538c7433129777506355e7d0c7474eefbcb50e
What was observed
{
"endpoints": [
[
"x402",
"https://data-calc.x402tookit.com/queue-model"
]
],
"name": "Systems Capacity Calculators",
"owner_address": "0xb531320805c5bed1d46aeadcf4f008fdf172dbda",
"raw": {
"accepts": [
{
"amount": "20000",
"asset": "0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913",
"extra": {
"name": "USD Coin",
"version": "2"
},
"maxTimeoutSeconds": 300,
"network": "eip155:8453",
"payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
"scheme": "exact"
},
{
"amount": "20000",
"asset": "EPjFWdd5AufqSSqeM2qN1xzybapC8G4wEGGkZwyTDt1v",
"extra": {
"feePayer": "D6ZhtNQ5nT9ZnTHUbqXZsTx5MH2rPFiBBggX4hY1WePM",
"transactionVersions": [
0
]
},
"maxTimeoutSeconds": 300,
"network": "solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp",
"payTo": "DUPiupXtuox38dcGoXUKer5mAydCzmaHjrbQ66qeEm8s",
"scheme": "exact"
},
{
"amount": "20000",
"asset": "0x3c499c542cEF5E3811e1192ce70d8cC03d5c3359",
"extra": {
"name": "USD Coin",
"version": "2"
},
"maxTimeoutSeconds": 300,
"network": "eip155:137",
"payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
"scheme": "exact"
},
{
"amount": "20000",
"asset": "0xaf88d065e77c8cC2239327C5EDb3A432268e5831",
"extra": {
"name": "USD Coin",
"version": "2"
},
"maxTimeoutSeconds": 300,
"network": "eip155:42161",
"payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
"scheme": "exact"
}
],
"description": "M/M/1 and M/M/c queue: utilisation, probability of waiting (Erlang C), queue length, wait and response time, tail odds.",
"extensions": {
"bazaar": {
"info": {
"input": {
"method": "GET",
"queryParams": {
"arrivalRate": 8,
"servers": 1,
"serviceRate": 10,
"waitThreshold": 0.5
},
"type": "http"
},
"output": {
"example": {
"asOf": "2026-10-11T20:19:39.979Z",
"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.",
"meanInSystem": 4.000000000000002,
"meanQueueLength": 3.2000000000000015,
"meanServiceTime": 0.1,
"meanTimeInSystem": 0.5000000000000002,
"meanWaitGivenWaiting": 0.5,
"meanWaitInQueue": 0.4000000000000002,
"model": "M/M/1",
"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"
],
"offeredLoadErlangs": 0.8,
"probabilityEmptySystem": 0.19999999999999996,
"probabilityNoWait": 0.19999999999999996,
"probabilityOfWaiting": 0.8,
"probabilityWaitExceedsThreshold": {
"probability": 0.2943035529371539,
"t": 0.5
},
"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"
],
"source": "computed locally (M/M/c queueing theory)",
"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%.",
"utilization": 0.8,
"verdict": "BUSY"
},
"type": "json"
}
},
"schema": {
"$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"
}
}
},
"lastUpdated": "2026-11-01T22:47:17.768Z",
"quality": {
"l30DaysTotalCalls": 2,
"l30DaysUniquePayers": 2,
"lastCalledAt": "2026-11-01T22:47:17.601Z"
},
"resource": "https://data-calc.x402tookit.com/queue-model",
"serviceName": "Systems Capacity Calculators",
"tags": [
"queueing",
"mm1",
"mmc",
"erlang-c"
],
"type": "http",
"x402Version": 2
},
"source": "x402_bazaar",
"summary": "M/M/1 and M/M/c queue: utilisation, probability of waiting (Erlang C), queue length, wait and response time, tail odds."
}What the leaf hashes
{"body":"6f015fbfb19510fe1f55b12c1d547ff24aa6d8d91dac930746960aa3db58a0be","id":2202005,"kind":"listing","method":"sync.x402_bazaar/1","observed_us":1793646811313458,"prev":null,"subject":"x402_bazaar:https://data-calc.x402tookit.com/queue-model","subject_kind":"source_record"}Proof
Fold these into the leaf in order, hashing each sorted pair with keccak256, to reach the root of (444186 rows).
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- Day root
- 0x78fecaabbe319e56f5c4b80fc02e2052e198ad24781da8832a475ff65f2002d1
- Chained
- 0xdc35957db5d1371ca382b9152878ffece28ec7c5cb4f98fd71ddb367f8b999b2
- Published
- On Arc Testnet, block 70432815: 0x56b814612eb2e3e544153df3e91e1f7199106d1e430c7d8c6b653feeb9ebe9af