The paper analyzes a stable queue that starts operating at time with customers. First, it analyzes the time required for this queue to empty for the first time. Under the assumption that both the interarrival and the service time distributions are of the exponential type, the paper proves that , where λ and μ are the arrival and the service rates. Furthermore, assuming in addition that the interarrival time distribution is of the non-lattice type, it shows that the settling time of the queue is essentially equal to ; that is, the paper proves thatwhere is the total variation distance between the distribution of the number of customers in the system at time t and its steady-state distribution. Finally, it shows that there is a similarity between the queue which is analyzed and a simple fluid model.
