This paper investigates a Generic Cell Rate Algorithm (GCRA) based Usage Parameter Control (UPC) function implementing a discard function for non-conforming cells, thereby establishing a so-called Cell Discard Ratio (CDR) as UPC performance measure. Focusing on Constant Bit Rate (CBR) connections, the UPC transfer characteristics are studied in case of Peak Cell Rate Contract Violations. Also the influence of the Contracted Cell Delay Variation Tolerance value on the CDR performance of the UPC is incorporated in the study. Algorithmic formulas found by analysis as well as simulation results are compared against the outcome of test-bed measurements. As opposed to the approach in the analysis, the simulation effectively takes into account the delay experienced by the cells accessing the ATM slotted medium, as sole origin of cell delay variation. The applicability of the simulation and the D. D. Kouvatsos (ed.