Queue Wait Time Calculator
Compare measured waits, steady-state Little’s law and declared M/M/1 or M/M/c queue models.
A QUICK WALKTHROUGH
How to use this tool
- Enter samples or choose an analytical model and its time unit.
- Declare assumptions, then add optional named scenarios.
- Calculate and inspect each formula, parsed input and limitations; copy or download the full report.
Limitations
Each line: nonnegative duration, optionally | censored; or ISO arrival | ISO service start. Missing service start is censored. ISO timestamps require Z or a numeric timezone offset. Censored waits are counted and excluded, never treated as zero. Percentiles use sorted completed waits with linear interpolation h=(n−1)p; completed-only statistics may be biased.
Limitations
Declare a stable observation window with consistent population, units and no accumulation for Little’s law. For M/M: Poisson arrivals, independent exponential service, identical servers, FIFO, infinite capacity/population, no abandonment and steady state. These assumptions are user declarations, not inferred from measured samples.
Limitations
Numeric decimal input: at most 256 characters and exponent magnitude ≤ 1,000; finite nonnegative binary64 values only, with nonzero underflow rejected. M/M requires μ > 0, λ ≥ 0, integer c from 1–1,000. Little requires λ > 0. At most 12 scenarios and 10,000 observation rows. Nonfinite derived results are rejected. Non-finite or underflowed model results are rejected rather than replaced by zero. Near-capacity results are sensitive to binary64 rounding. Processing is bounded by sorting 10,000 samples and at most 1,000 Erlang recurrence steps per scenario.
GOOD TO KNOW
Common questions
How are incomplete waits handled?
They remain counted as censored or unknown. Completed-only mean and percentiles do not estimate the censored distribution.
Does the model recommend staffing?
No. Enter c yourself. M/M values depend on declared assumptions and do not predict actual operations.
How do queue and system measures differ?
Lq/Wq exclude service; L/W include service. Little’s law uses the same scope on both sides.