The Directed Acyclic Graph(DAG) scheduling algorithm

based on time-constrained and minimum-cost in grid environment

applies economic law to map the running tasks of grid users into grid resources.The proposed algorithm overcomes the deficiency of Buyya R's algorithm

which is not concerned with priority relationship between running tasks.It is highlighted in two key techniques:one is that the extraction of valid paths from DAG can effectively locate tasks in specific resources during specific periods;the other one is that tasks should be mapped into cheap resources so that they can be run as much as possible with the restriction of job-running time.A simulative example based on the algorithm is also provided to analyse the characteristics of the algorithm.