In the future, Broadband Integrated Services Digital Network (B-ISDN) is expected to serve voice, video, data and other signals in a single network. Asynchronous Transfer Mode (ATM) and Internet have emerged as two competing networking architectures for the realization of B-ISDN. There is a need to provide support for service differentiation in both network architectures. An important network device for service differentiation is the scheduling algorithms implemented at the switch and router queues.  The objective of this thesis has been to provide a comprehensive performance study of these scheduling algorithms. The main scheduling algorithms are First In First Out (FIFO), Priority Queueing (PQ), Fair Queueing (FQ) and Weighted Round Robin (WRR) service disciplines. Several derivatives of these algorithms were introduced with varying efficiency and complexity. We compare these algorithms and their derivatives with respect to mean message delay, probability distribution of delay and call blocking probability performance measures. (Abstract shortened by UMI.)