Work out queue servers required instantly with clear inputs, formula shown and shareable results.
Offered load in erlangs is arrival rate multiplied by service time, and the number of servers must exceed it for the queue to be stable. Servers are then added until the estimated wait meets the target, because waiting time explodes non-linearly as utilisation approaches 100%.
Offered load
Load (erlangs) = Arrivals per hour x Service minutes / 60
Starting point
Servers = ceiling(Offered load / Target utilisation)
Wait approximation
Wait = Service time x Utilisation / (Servers x (1 - Utilisation)), with servers increased until the wait target is met
Because arrivals are random. With no slack, a short cluster of arrivals creates a queue that never fully clears before the next cluster.
Usually the two servers, because they absorb variability better even at the same total capacity. Pooling queues has the same effect.