In an automatic call distribution (ACD) system, an improved estimated waiting time arrangement derives a more accurate estimate of how long a call that is or may be enqueued in a particular queue will have to wait before being serviced by an agent, by using the average rate of advance of calls through positions of the particular queue. For a dequeued call, the arrangement determines the call's individual rate of advance from one queue position to the next toward the head of the queue. It then uses this individual rate to recompute a weighted average rate of advance through the queue derived from calls that preceded the last-dequeued call through the queue. To derive a particular call's estimated waiting time, the arrangement multiplies the present weighted average rate of advance by the particular call's position number in the queue. The arrangement may be called upon to update the derivation at any time before or while the call is in queue. Also, the arrangement performs the estimated waiting time derivation separately and individually for each separate queue. The arrangement advantageously takes into consideration the effect of ACD features that affect the estimated waiting time, including changes in the numbers of agents that are serving the queue due to agent login and logout, multiple split/skill queuing, agents with multiple skills or in multiple splits, priority queuing, interflow, intraflow, and call-abandonment rates.