Work out waiting time in queue instantly with clear inputs, formula shown and shareable results.
Waiting time follows from Little's law applied to the M/M/1 queue: the wait is utilisation divided by capacity times one minus utilisation. Because the wait depends on one minus utilisation, adding a small amount of capacity at a busy till cuts waiting time far more than it cuts utilisation.
Average wait
Wq = rho / (capacity x (1 - rho))
Time in system
W = Wq + 1 / capacity
Wq = rho / (capacity x (1 - rho)). Waiting time follows from Little's law applied to the M/M/1 queue: the wait is utilisation divided by capacity times one minus utilisation.
Because the wait depends on one minus utilisation, adding a small amount of capacity at a busy till cuts waiting time far more than it cuts utilisation.
Enter arrivals per hour, customers one server handles per hour, number of servers. The defaults shown are a realistic worked example — swap in your own figures to get a result you can use.