Source: https://guthlabs.ai/docs/instruments/load-balancer-queueing-wait-time-estimator-m-m-1/implementation/

instrument implementation / implementation-contract

# Load Balancer / Queueing Wait-Time Estimator (M/M/1) implementation

A source-bound implementation contract for Load Balancer / Queueing Wait-Time Estimator (M/M/1); deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t5-069

**Effect**: Computation or source lookup only

## Input and validation requirements

The specification becomes unsafe if an implementation blindly evaluates L and W at or above ρ=1: at equality it divides by zero, and above equality it can emit negative queue lengths and wait times unless it rejects the unstable case. Mixed rate units can also produce incorrect utilization and stability decisions if rates are not normalized.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "arrival_rate_lambda": 2,
    "service_rate_mu": 5,
    "rate_unit": "jobs/second"
  },
  "expected_outputs": {
    "utilization_rho": 0.4,
    "instrument_formula_L": 0.666666667,
    "correct_average_queue_length_Lq": 0.266666667,
    "instrument_formula_W_seconds": 0.333333333,
    "correct_average_queue_wait_Wq_seconds": 0.133333333,
    "stability_warning": false
  },
  "working": "ρ=λ/μ=2/5=0.4. Supplied L=ρ/(1−ρ)=0.4/0.6=0.666666667. Correct Lq=ρ²/(1−ρ)=0.16/0.6=0.266666667. Supplied W=1/(μ−λ)=1/(5−2)=1/3=0.333333333 seconds. Correct Wq=ρ/(μ−λ)=0.4/3=0.133333333 seconds."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/load-balancer-queueing-wait-time-estimator-m-m-1/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/load-balancer-queueing-wait-time-estimator-m-m-1/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/load-balancer-queueing-wait-time-estimator-m-m-1/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche5/tranche5-results.json`