Random Waiting-Time Experiment Generator
Use the existing seed-only exponential sampler once for the entire IID waiting-time experiment batch, retaining observations and model mean. Explicit seed required; injected sources rejected rather than silently ignored or restarted per sample. Rate/time units reciprocal; no actual service-delay inference.
Description
Exponential waiting-time simulations use a declared rate whose reciprocal is the model mean.
Exponential waiting-time simulations use a declared rate whose reciprocal is the model mean.1
Simulated observations describe that model rather than actual service or event delays.
When to use Random Waiting-Time Experiment Generator
Use this tool when you need to produce the reproducible draw or model experiment described below. Prepare the seed and the exact inventory or scenario inputs described below. Keep units, reference edition, and sampling convention explicit.
How to use Random Waiting-Time Experiment Generator and understand its results
- Prepare the seed and the exact inventory or scenario inputs described below. Keep units, reference edition, and sampling convention explicit.
- Enter seed, count, rate, following the field table and calculation rules below, then run the tool.
- Read result. Inspect the nested fields in the output table below and keep any missing evidence or selected indices visible.
- Correct any input issues and run again. Before using a successful result, review its units, signs, evidence coverage, and stated model or reference assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| seed | Nonblank reproducibility seed; default seeded runs restart for each request | string | Required |
| count | Number of simulated replicates | safe integer from 1 to 64 | Required |
| rate | Rate | number | Required |
Require a nonblank seed of at most 256 units, safe-integer count in [1,64], and positive rate. Reject an injected context.random source. Call probability/exponential-sampler once for the whole batch using the seed, preserve its samples, and return their mean and model mean 1/rate. The whole-batch seed is not restarted for each sample. The imported sampler creates one seeded stream and applies its inverse-CDF expression to each draw, using log1p for numerical stability.2, 3, 4
sample=−ln(1−U)/rate; modelMean=1/rate Read these symbols with the field meanings and branch or reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the fields below | object |
| result.samples | Simulated values in replicate order | list |
| result.observedMean | Arithmetic mean of the simulated samples | number |
| result.modelMean | Declared model expectation; not an estimate of real events | number |
| result.samplingConvention | Sampling Convention | string |
{
"input": {
"seed": "tool.io/batch42",
"count": 1,
"rate": 2
},
"output": {
"result": {
"samples": [
1.1822449389767555
],
"observedMean": 1.1822449389767555,
"modelMean": 0.5,
"samplingConvention": "independent-exponential-rate"
}
}
}Limitations and assumptions
The default source is deterministic pseudorandomness, not an independently audited or secure draw. Replacement applies to inventory positions; distinct positions may render identically or yield equal answers. Review the supplied inventory or scenario domain independently before interpreting the sample.
Missing required fields, unknown fields, wrong types, and violated calculation rules return input issues. Numeric values must be finite; nonfinite numeric outputs are rejected. Extremely large composite outputs are rejected.
Alternative or Complementary methods
For a related task, use Random Poisson Count Experiment Generator: A Poisson count model specifies an event-rate parameter for the modeled interval. Simulated samples and their mean can be compared with the model mean and variance without deciding a hypothesis test. For a complementary step, use Random Normal Quantile Coverage Experiment Generator: Normal-model coverage experiments compare simulated standardized values with declared interval bounds. Observed coverage is a finite-sample statistic rather than a calibrated confidence level.
References
Similar or alternative tools
- Random Poisson Count Experiment Generator
A Poisson count model specifies an event-rate parameter for the modeled interval. Simulated samples and their mean can be compared with the model mean and variance without deciding a hypothesis test.
- Random Normal Quantile Coverage Experiment Generator
Normal-model coverage experiments compare simulated standardized values with declared interval bounds. Observed coverage is a finite-sample statistic rather than a calibrated confidence level.