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In this paper, we present a new approach to schedule malleable requests over grid computing networks. The proposed solution called MS-DFGA (MS-DFGA: Malleable Scheduling with Dynamic MaxFlow and Greedy Algorithms) aims at maximizing the network utilization while increasing the requests acceptance ratio. We have adapted Multi-constrained Knapsacks Problem (MKP) to the malleable requests scheduling, and propose a solution to resolve it. MS-DFGA is performed in two steps. The first step corresponds to the computation of the candidate paths over the network using a Dynamic MaxFlow algorithm. The second step concerns the malleable requests scheduling over these paths. The paths represent the knapsacks, and the requests correspond to the items of the MKP problem. Also, we present an implementation of our solution as a new simulator framework which we have developed in a JAVA environment. Moreover, simulation results illustrate the efficiency of our scheduling method to: provide guarantees for critical grid traffics with timely execution requirements, avoid bandwidth wastage when the temporal constraints are too close and hence reducing the blocking ratio.