**Abstract** Queuing Theory deals with the mathematical consideration of waiting queues. This paper simulates a M/M/1 queue, which is the simplest model in Queuing Theory, with the help of the server software Rabbit MQ. Thereby the average number of users in the queuing system and in the queue is measured. Furthermore the average time in the queuing system per user and the waiting time in the queue per user is calculated. The resulting values of 25 runs are compared to the expected values of the equations by the Queuing Theory. The results show that the expected value is nearby the mean of the simulation and most likely in the 95% confidence interval around the mean value. Moreover the FIFO property of M/M/1 queues is confirmed.