The present invention focuses on the aggregation of flows belonging to different classes of non-guaranteed-delay traffic into a single FIFO queue in a downstream stage of the multi-stage switch. These include the guaranteed flows requiring bandwidth reservation, the best-effort flows that require a fair share of the excess bandwidth, and the flows that require both types of guarantee. We disclose a credit-based backpressure scheme which selectively controls the traffic originating from the previous stage of the system while achieving the goal of meeting the requirements of the individual flows. The credit function is maintained for each controlled traffic component in the aggregate session, and its objective is to balance the actual arrival rate of the component with the service rate dynamically granted by the downstream scheduler. The number of flows that can be aggregated is related to the complexity of maintaining the credit functions for the different traffic components.