The ATM Forum defined the guaranteed frame rate service category to provide a minimum service guarantee to classical best-effort services. The eligibility of frames for this service category is determined with the frame based generic cell rate algorithm and the transmission is guaranteed by a queuing-discipline based on two thresholds. We present a discrete-time analysis of the GFR-service under the assumption of constant available bandwidth. The presented method can be applied to dimension the thresholds of the queuing discipline used to enforce the guaranteed service.