In this paper, we propose a generalized longest first (GLQF) service discipline for ATM networks. We classify sources so that sources in one class have the same cell loss probability requirement. Assume that there are N classes of traffic. Under this discipline, buffer i is assigned a positive number wi for the weight of buffer i. The scheduler transmits a cell from the buffer that has the maximal weighted queue length. The advantage of this discipline is that it can adapt to temporary overload quickly. We approximate the queue length distribution by decomposing the system into N single server queues with probabilistic service discipline. Our method is an iterative one, which we prove to be convergent by using stochastic dominance arguments and the coupling technique. For high utilization, we present a heavy traffic limit theorem.