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As network capacities increase, wide-area distributed parallel computing may become feasible. This paper addresses one of the issues involved in using an asynchronous transfer mode (ATM) network for such a purpose — that of developing an appropriate call admission control (CAC) procedure for such applications given the special nature of their traffic. In this proposal, connections belonging to the same application and sharing the same link are allowed to utilize the linkbandwidth in a strongly correlated manner. However, connections belonging to different applications are still assumed to be independent. This allows the development of a tabular approach for keeping track of the aggregate bandwidth demand of the applications sharing the same link. The proposed approach is compared with two related approaches (one more conservative and another more aggressive) and is shown to strike a balance between utilization and loss rate.