The ATM Forum recommends the use of the Generic Cell Rate Algorithm (GCRA) to perform Usage Parameter Control at the User Network Interface of ATM networks. In order to facilitate the Call Admission Control and resource allocation procedure, it is important to investigate the characteristics of the model in which GCRA-enforced sources are merged together by a multiplexer. Such a multiplexer could be the one arranged in front of a switch to concentrate user traffic and reduce the number of required input ports. It may also represent the logical multiplexer at the output port of a switch that collects cells routed from various input ports. Moreover, it may represent the service function of the edge router situated between the integrated-services (IntServ) networks and the backbone networks that provide differentiated-services (DiffServ). In this paper, the environment under discussion is a multiplexer in which every traffic source is enforced by a dual-stage GCRA enforcer before being merged. The worst traffic pattern that maximizes the average waiting time in the multiplexer is found. The maximum average waiting time is deduced and expressed as a function of the GCRA parameters and the number of multiplexed sources. In particular, the analysis considers the speed-up function, which is widely used for ATM multiplexers and switches. The results can also be applied to a GCRA shaper without any modification.

In ITU-T Recommendation I.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 '93 to define Sustainable Cell Rate and Burst Tolerance so as to facilitate Usage Parameter Control and Network Parameter Control. To judge the validity of a cell according to declared GCRA parameters, the enforcer must read the clock time when the cell arrives. However, the clock of the enforcer would roll over frequently and accordingly the judgment would be incorrect. On the other hand, for a shaper in a customer premise node to dispatch cells conforming to the declared GCRA parameters, the clock would also roll over and the cell would not be dispatched correctly. To overcome the problems induced by clock roll-over, based on "time difference" concept, we propose two modified GCRA's for the enforcer and shaper, respectively. According to the proposed algorithms, we design a feasible architecture for a multi-connection shaper and simplify it for an enforcer. They are proven to perform well in spite of the inherent clock roll-over characteristics. By simulation, we evaluate the delay in the shaper and the loss in the enforcer. The features of the architectures are also discussed.