Queue Wait Time Calculator

This calculator uses the M/M/c queueing model -- the standard formula for a line fed by one shared queue and served by multiple parallel service points, like ticket windows or ride turnstiles -- to estimate how long visitors wait. All three inputs move Server Utilization by an equal share: Arrival Rate raises it, while Service Rate and Service Points each lower it by the same proportional amount, since utilization is simply Arrival Rate divided by their product. Wait time, by contrast, does not respond smoothly to Service Points the way it does to Arrival Rate or Service Rate -- it's a genuinely discrete count of ticket windows or turnstiles, and the underlying formula only accepts whole numbers. At the default inputs (Arrival Rate 100/hr, Service Rate 40/hr, 3 Service Points), utilization sits at 83.3%; drop to just 2 Service Points and utilization crosses 100%, meaning the queue is modeled as growing without bound -- the calculator shows a capped placeholder rather than a real wait time once that happens.

That's a far more dramatic effect than a smooth percentage change would suggest, and it's the reason Service Points deserves special attention rather than a simple side-by-side comparison with the other two inputs. Service Time (the average time to serve one visitor) responds only to Service Rate -- neither Arrival Rate nor the number of Service Points changes how long a single transaction takes. This is a steady-state model; it assumes a constant arrival pattern and doesn't account for real-world bursts, breaks, or visitors who abandon a long line.