Estimate average queue wait for a simplified emergency department treatment stage using arrival rate, staffed treatment spaces, and average treatment time. The model also shows space occupancy, the chance an arriving patient must wait, average queue length, and the gap to a user-set occupancy target. Use it for directional scenario comparison—not for triage, clinical prioritization, or a promise of individual wait time.
The main result is the modeled average time in queue before a treatment space becomes available. The probability of waiting distinguishes a short average wait from a system where many arrivals still encounter a queue.
The M/M/c model assumes random independent arrivals, exponential service times, identical parallel spaces, one queue, no abandonment, and no priority classes. Emergency departments often violate these assumptions; validate against observed data.
With 4 arrivals per hour, 18 staffed spaces, and 180 minutes per treatment, each space serves 0.333 patients per hour. Total service capacity is 6 per hour and modeled occupancy is 66.67%. The Erlang C estimate is approximately 2.30 minutes of average queue wait.
The steady-state queue is unstable, so the calculator reports that no finite average wait can be estimated.
Only if that time is included in the treatment-time input and uses the same constrained spaces.
Many arrivals may wait briefly when capacity frees quickly; the two measures describe different aspects of the queue.
You can, but peak-hour scenarios are usually more informative because queues are nonlinear.
No. It assumes one first-come operational queue and must not be used for clinical prioritization.
| Input | Model role | Unit |
|---|---|---|
| Arrivals | Average demand rate λ | Patients/hour |
| Spaces | Parallel servers c | Count |
| Treatment time | Inverse of service rate μ | Minutes |