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In this paper, we present a novel control-theoretic explicit rate (ER) allocation algorithm for congestion control of available bit rate (ABR) service in high speed computer communications networks. The proposed control uses a proportional-integral-plus-differential (PID) controller rather than the usual adopted proportional-plus-differential (PD) controller. Based on a general traffic model of the computer network and on the system criterion, it is shown that under a PID controller the source rates are regulated in such a manner that the congestion-controlled network is asymptotically stable in terms of both the buffer occupancy of the destination node and the user transmission rates, and the bandwidth fairness is achieved. The basic control theory approach for the algorithm is firstly presented; specifically the z-transformation and Schur-Cohn stability test are used to achieve the stability. Steady state analysis is subsequently given to show how the max/min fairness is achieved in a natural way without additional computation. We then use simulations to compare the performance of the PID congestion control scheme with the PD control scheme under a variety of networking conditions and loads. Our simulation results show that certain PID scheme produces advantages over PD scheme, namely PID control scheme leads to less buffer occupancy, faster response of the buffer occupancy as well as of the controlled ABR rates, smaller steady overshoots of ABR traffic and better utilization of network links.