A queue is not evidence that you lack capacity. Set the service desk to serve faster than customers arrive, press play, and watch: with no randomness, nobody ever waits. Add randomness — the same arrival rate, the same service rate — and the line appears.
Customers waiting, over simulated time. With no variability and utilization below 1, this line never leaves zero.
Interarrival and service times are drawn from gamma distributions matched to the mean and coefficient of variation you set, so CV = 0 is clockwork, CV = 1 is exponential, and above 1 is burstier than exponential. Leave the seed blank for a fresh run each time, or set one so a whole class faces the same customers.