An analytical formulation of the transient behavior of the available bit rate (ABR) explicit-rate traffic flow control for the single-node case is presented. Precisely, the transient effects due to available capacity increasing (a ramp-up) of the previously proposed distributed explicit-rate allocation (DERA) scheme, and generally valid available capacity decreasing (a ramp-down) transient case are analytically formulated, using fluid-flow traffic approximation. An analytical formulation of the queue build-up, and characteristic time instants provides an insight of the cause and effect relationships, and can be used for buffer dimensioning. In addition, quantification of the queue build-up and the dependence on other system parameters may prove useful in evaluating other algorithms and designing those that avoid it. The obtained analytical results are verified through discrete-event simulation.