Simulate an M/M/1 queue in which customers arrive at the rate of three per hour and are served at the rate of five per hour:

Since the arrival rate is less than the service rate, the system reaches a steady state:

If the arrival rate is greater than the service rate, then the system does not reach a steady state:

Simulate a queueing system that can hold only 12 customers:

Simulate a queue with 20 customers in the initial state: