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An estimation of task resource demands is an important area of research in Grid computing. Efficiency of managing and planning resources and tasks in heterogeneous computer systems depends heavily on the accuracy of estimating each task resource demands. In this paper we explain how building the task work path for one fixed background loading and approximating the task resource consumption is applied to the resource consumption estimate for the tasks running in the GRID environment. In addition we address dimensional blowout by approximating the CWG matrix based on Markov clustering. This technique allows us to essentially reduce the resources and experiment time which are required for invariant generating and to make application of the method to the GRID scheduling and planning a reality.