Up till now (Chu [1], Rudin [3]), the overflow probabilities of a hold-and-forward concentrator have been determined assuming that the pooled traffic of a number of terminal users at the input of the concentrator has a completely independent interarrival statistic between the characters. A closer analysis of the data going from one user to a computer shows that the user burst segments are separated in time by the total sum of idle time, computer burst segment time, and think time. Therefore, the interarrival statistic between two user burst segments cannot be of the negative exponential type. Starting from a more realistic interarrival statistic, it then follows that the interarrivals for the pooled user traffic are dependent. With this new model, the overflow probabilities have been determined as a function of the number of user terminals, traffic intensity, buffer capacity, and user terminal statistics.