According to the ITU-T Recommendation 1.371, the Generic Cell Rate Algorithm (GCRA) is used to define Peak Cell Rate for the ATM network. It is further applied by the ATM Forum to define Sustainable Cell Rate and Burst Tolerance so as to facilitate Usage Parameter Control and Network Parameter Control. To check the validity of a cell according to the declared traffic parameters, the enforcer must read the clock time when a cell arrives. However, the clock of the enforcer would roll over frequently and thus makes wrong judgment. On the other hand, for a shaper in a customer premise node to dispatch cells conforming to the declared parameters, the clock would also roll over and the cell would not be dispatched correctly. To overcome the problems introduced by clock roll-over, we propose two modified GCRAs for the enforcer and the shaper, respectively. According to the proposed algorithms, we design new architectures for multi-connection shapers and enforcers in which a cell's priority is also considered. We also prove that the proposed algorithms are justified for the proposed architectures.