It is not a simple and trivial work to set up an appropriate network traffic model. A fractional Alpha model is proposed in this paper and two proofs based on flow and session level, respectively, are given. Based on this model, the lower bound for the residual of the queueing distribution is deduced. Comparing the residual distribution function (RDF) based on our model with it based on other models, we find our formula matches the real RDF better. Based on this formula, we can predict the need for forwarding performance. Then a novel QoS routing algorithm based on this prediction is proposed. Last we demonstrate a simple example to denote how our algorithm can effectively improve the utility of bandwidth and amount of traffic and guarantee QoS.