Enter how many visitors arrive in your busiest hour, how many minutes one check-in takes and how many desks or kiosks are open. The calculator shows how busy each desk is, how long the average visitor waits and the fewest desks that keep the wait under your target.
The calculator treats the reception desk as an M/M/c queue: visitors arrive at random, check-in times vary around their average, every desk can serve any visitor, and visitors wait rather than leave. It is the same waiting-probability model (Erlang C) that is used to size call handling, applied here to people at a counter.
The script computes P(wait) through the equivalent Erlang B recursion rather than raw factorials, so large numbers do not overflow; the result is the same.
Suppose 30 visitors arrive in the busiest hour, each check-in takes 4 minutes, and 3 desks are open. The offered load is 30 × 4 ÷ 60 = 2 desks busy on average, so utilisation is 2 ÷ 3 = 67%. The probability of waiting works out to about 44%, and the average wait is 0.444 × 4 ÷ (3 − 2) ≈ 1.8 minutes. With only 2 desks, utilisation would be 100% and the queue would keep growing until arrivals slowed. The figures are illustrative; use counts from your own register or gate log.
Adding desks is one lever; shortening each check-in is usually cheaper. Every minute removed from the average lowers the load on every desk at once. Pre-registering visitors, so the desk confirms details instead of typing them, and moving inductions out of the peak hour both reduce the check-in time you enter above.
Sampark is gate pass and visitor software for plants, mines and townships that shortens the check-in itself: approved visitors are already on the gate’s digital expect list with a QR, so at the desk the QR is scanned, ID matched, and the host and room are alerted without phone calls from the booth. For the wider process, read the playbook for clearing the night queue at the gate and the guide to visitor management at industrial sites.
Work out the offered load (arrivals per hour × minutes per check-in ÷ 60), then use an M/M/c queueing formula with the number of desks to get the probability of waiting and the average wait. The calculator on this page does the arithmetic.
Enough that utilisation stays clearly below 100% in the busiest hour and the average wait meets your target. Enter your peak arrivals and check-in time, set a target wait, and the calculator returns the fewest desks that meet it.
It depends on what the desk does: a pre-registered visitor with a QR can be confirmed quickly, while a walk-in needing ID capture, a printed pass and a safety briefing takes much longer. Time your own desk over a peak and use that average.
Visitors do not arrive evenly. As utilisation approaches 100%, a short burst of arrivals builds a line that takes a long time to clear, so the average wait rises sharply even when desks are sometimes idle.
See it on your own data. Sampark — Every desk and guest, one spine. Book a 30-minute working session with an engineer.
