A system is disclosed which services a plurality of queues associated with respective data connections such that the system guarantees data transfer rates and data transfer delays to the data connections. This is achieved by associating each connection having at least one data packet waiting in its associated queue (such a connection called a backlogged connection) with a timestamp generated as a function of system parameters including (a) the number of queues that are backlogged, (b) the data transfer rate guaranteed to each connection, (c) the sum of data transfer rates guaranteed to all backlogged connections, (d) the previous timestamp of the connection, and (e) the weighted sum of the timestamps of all backlogged connections, each timestamp weighted by the data transfer rate guaranteed to the corresponding connection. The backlogged connection associated with the timestamp having the smallest value among all of the backlogged connections is then identified and a data packet is transmitted from the queue corresponding to that connection. A new timestamp is then generated for that connection if it is still backlogged. Once the transmission of the data packet is completed, the foregoing determination of the connection with the minimum timestamp is then repeated to identify the next queue to be serviced.