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Example /hour min hours
People waiting over timeRun to see this
If you change the number of servers
ServersUtilisationAvg waitLongestWaited 10min+
Results
Nothing calculated yet
Enter the conditions and press Run.
Enter the conditions and press Run. Nothing is sent anywhere.
How to use: enter how many people arrive per hour, how many minutes each takes, and how many servers you have, then press Run. Utilisation is the share of time your servers are busy, and the wait climbs steeply as it approaches 100%. Up to about 70% there is slack; past 90% a small fluctuation is enough to stretch the queue out. Set variability to "always the same" to compare against the ideal case of a perfectly constant service time — with the same average, variability alone can nearly double the wait. Nothing you enter is sent to a server. The maths and the chart run in your browser.
If you need to actually run the reception and call-up side of a queue, see our Narabi (queue and reception management). Our free learning posters explain data and web concepts with diagrams.
Related tools: Color Code Converter Number Base Converter Check Digit Calculator Kansuji Converter

Frequently asked questions

How much does adding one more server cut the wait?

It depends entirely on how busy you already are. Below about 70% utilisation an extra server barely changes what customers feel, but adding one where utilisation is above 90% can cut the wait to a fraction. Queues grow explosively as utilisation approaches 1. This tool lists the average wait for a range of server counts side by side, so you can see whether adding one is worth it.

How realistic are the results?

They assume arrivals are completely random (Poisson) and service times follow an exponential distribution. Real shops have lunchtime peaks and customers who give up and leave, so the numbers will not match exactly. Use this to see the direction of an effect: whether adding a server helps, or whether shortening service time helps more. Switching variability to "fixed" shows the ideal case where every customer takes exactly the same time.

Why do the simulation and the theoretical value differ?

The theoretical figure (the Erlang C formula) is the long-run average of a system that runs forever in steady state. The simulation queues real customers for exactly the opening hours you entered, so it includes the quiet stretch after opening and the luck of a busy day. Longer hours bring it closer to theory. Near 100% utilisation the theoretical value itself diverges, so a large gap there is expected.

Are the numbers I enter sent to a server?

No. The simulation, the maths and the chart all run inside your browser. Nothing you type is sent anywhere or stored. The page uses no external libraries at all.