Queue Model

{
  "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"
}

# bash or zsh: see the payment challenge. Nothing is charged.
curl -sS -g -i 'https://data-calc.x402tookit.com/queue-model?arrivalRate=8&servers=1&serviceRate=10&waitThreshold=0.5'

# x402 v2 sends the challenge base64-encoded in the PAYMENT-REQUIRED header (v1 sends it in the body).
# To read the header:
curl -sS -g -o /dev/null -D - 'https://data-calc.x402tookit.com/queue-model?arrivalRate=8&servers=1&serviceRate=10&waitThreshold=0.5' \
  | grep -i '^payment-required:' | cut -d' ' -f2 | tr -d '\r' | base64 --decode

// npm i @x402/fetch @x402/evm viem
import { wrapFetchWithPayment, x402Client } from "@x402/fetch";
import { registerExactEvmScheme } from "@x402/evm/exact/client";
import { privateKeyToAccount } from "viem/accounts";

// Pays at most $0.02 per call.
const client = new x402Client().setSpendControls({ maxAmountPerPayment: "$0.02" });
registerExactEvmScheme(client, { signer: privateKeyToAccount(process.env.EVM_PRIVATE_KEY) });
const pay = wrapFetchWithPayment(fetch, client);

// Not sure it's safe to pay? ToolVet checks it first for $0.005. Pay for that from a separate
// client: this one is capped at $0.02 per payment. GET https://toolvet.app/api/v1/check?url=https%3A%2F%2Fdata-calc.x402tookit.com%2Fqueue-model
const res = await pay("https://data-calc.x402tookit.com/queue-model?arrivalRate=8&servers=1&serviceRate=10&waitThreshold=0.5");
console.log(res.status, await res.text());

# pip install "x402[requests,evm]"
import os
from eth_account import Account
from x402 import x402ClientSync
from x402.http.clients import x402_requests
from x402.mechanisms.evm import EthAccountSigner
from x402.mechanisms.evm.exact.register import register_exact_evm_client

# Pays at most $0.02 per call.
client = x402ClientSync().set_spend_controls({"max_amount_per_payment": "$0.02"})
register_exact_evm_client(client, EthAccountSigner(Account.from_key(os.environ["EVM_PRIVATE_KEY"])))

with x402_requests(client) as session:
    res = session.get("https://data-calc.x402tookit.com/queue-model?arrivalRate=8&servers=1&serviceRate=10&waitThreshold=0.5")
    print(res.status_code, res.text)