Disclosed is a weighted longest queue first (WLQF) service discipline for ATM networks. The sources are classified so that sources in one class have the same cell loss probability requirement. For N classes of traffic the WLQF system has N buffers to store the traffic, wherein buffer i is assigned a positive number w.sub.i for the weight of buffer i. The scheduler transmits a cell from that buffer whose index maximizes w.sub.i Q.sub.i for i=1, 2, . . . ,N, where Q.sub.i is the queue length of buffer i at the moment when the scheduler makes a decision about which buffer to serve. Accordingly, the inventive system always serves the most congested buffer relative to the weighted queue lengths, and can adapt to temporary overload quickly. This feature ensures that in temporary overloads of one of the buffers, the overloaded buffer, receives almost all the service and therefore, losses due to buffer overflows and cell delay variation (CDV) are much small. Additionally, when a call is received, the system determines whether it can provide the requested QoS, and rejects the call if not.