A lower average latency can hide more missed deadlines
The test of Distributed Failure Is a Latency Problem, Theory 062 in Volume VIII of the Incoprea research notebook, gives a clear mathematical example: a service with the lower mean latency can miss a fixed deadline much more often. That example is publishable after narrowing its interpretation. The calculation compares two assumed latency distributions; it does not test utilisation, overload, or a retry-driven outage.
Evidence classification: exact probability calculation for two assumed distributions. This minimally adjusted report corrects numerical presentation. No service was measured and the original causal hypothesis remains untested.
The supplied comparison
Service A has lognormally distributed latency with median 80 milliseconds and log-space standard deviation 1.3. Service B has median 246 milliseconds and log-space standard deviation 0.12. Both face a 500-millisecond timeout. A request fails when its latency exceeds that timeout.
These parameters describe a broad distribution for A and a tightly concentrated distribution for B. The NIST lognormal reference gives the distribution's interpretation and probability formulas. For median m and log-space standard deviation s, the model has mean m exp(s²/2), and its deadline-miss probability is
P(L > T) = 1 − Φ[ln(T/m)/s],
where Φ is the standard normal cumulative distribution function. The reviewed public reproduction evaluates the equivalent complementary-error-function expression, avoiding cancellation when a very small positive tail is subtracted from one.
| Assumed service | Mean latency | Probability of exceeding 500 ms |
|---|---|---|
| A: median 80 ms, s = 1.3 | 186.2 ms | 0.0793174, about 7.93% |
| B: median 246 ms, s = 0.12 | 247.8 ms | about 1.704 × 10⁻⁹ |
A has the lower mean and median, yet its stipulated distribution places much more probability beyond the selected deadline. These are calculated probabilities, not observed failure counts. B's probability is extremely small, rather than exactly zero; rounding it to five decimal places in the supplied headline statistics hid that distinction.
What the reproduction confirms
The original code also evaluates forty equally spaced timeout values from 150 to 1,200 milliseconds. An isolated run of the unchanged supplied script matched its saved results. The portable public version retains the same distributions, deadline and timeout grid. It only uses the numerically stable survival expression and removes unsupported verdict language from the public output.
The original expression, one minus the cumulative probability, loses some tiny B probabilities to floating-point cancellation at larger timeouts. The stable expression preserves positive values. This improves numerical reporting without changing the model or its central comparison at 500 milliseconds.
The timeout sweep also shows why there is no universal ranking of the two distributions. At 150 milliseconds, B misses almost every deadline because that deadline lies well below its median; A's miss probability is approximately 0.314. The comparison depends on the deadline being evaluated. A smooth probability curve does not establish a sharp system instability threshold.
Why this does not establish a low-load outage
The original hypothesis proposes a feedback mechanism: missed deadlines trigger retries, additional requests increase load, and latency worsens. None of those feedback steps appears in this calculation. Mean latency is not a measure of utilisation, and the code contains no arrival rate, capacity, queue, or utilisation variable. Calling A a low-utilisation service and B a busy service would therefore overstate the result.
The script also names a variable RETRIES but sets it to one and uses it as the total number of attempts. The reported result is for one attempt, with no retry. Raising a single-attempt failure probability to the number of attempts would describe failure on every attempt only under independent attempts with an appropriate success rule. It would omit added load, shared slowdowns, retry delays and the overall deadline. That count is not varied, leaving the retry prediction untested.
Tail latency is an established systems concern. Dean and Barroso's The Tail at Scale discusses its significance for large services and techniques for limiting its effects. That primary source provides context; it does not make the two hypothetical distributions representative of any real deployment.
The supported finding is consequently precise: an average alone does not determine the fraction of requests missing a deadline. Distribution shape and the chosen deadline matter. These assumptions demonstrate that possibility, while measurement and an explicit feedback model would be needed to assess a real outage mechanism.
Credit and reproducibility
The distributions, parameter choices, timeout sweep and original report were supplied in the DeepSeek-assisted Incoprea Probable Tests bundle dated 30 October 2026. Codex reviewed the posted hypothesis, reproduced the supplied calculation, corrected small-tail presentation and narrowed the conclusions. This publisher review is not external peer review and makes no novelty claim. Original code and results are preserved alongside the reviewed public reproduction and display results.