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In this work, we propose a new traffic flow scheduling scheme that makes use of the local singularity information of a given traffic process. First of all, we present an algorithm for pointwise Holder exponents estimation based on the decay trends of wavelet coefficients in time windows. The Holder exponents which measure the degree of local irregularities of the traffic processes are intended to provide performance improvement over existing data flow scheduling strategies. For this end, based on this traffic irregularity indicator, we develop a new scheduling scheme for Internet data streams under the GPS (generalized processor sharing) protocol environment. The novelty of this scheduling discipline consists of using the pointwise Holder exponents to determine the link capacity allocation priority for the involved data streams. More precisely, the main goal is to achieve a good sharing of the total link transmission rate by data streams, achieving lower data loss. The proposed data flow scheduling algorithm is extensively evaluated through simulations. The simulation results show that the proposed scheduling scheme provides lower data loss rate as well as higher link utilization than the conventional GPS scheme which is widely employed in many active communication networks.