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Reconfigurable processors in distributed grid systems can potentially offer enhanced performance along with flexibility. Therefore, grid systems, such as TeraGrid, are utilizing reconfigurable computing resources next to general purpose processors (GPPs) in their computing nodes. In general, the application task scheduling largely affects the near-optimal performance of resources in distributed grid systems. The inclusion of reconfigurable nodes in such systems requires to take into account reconfigurable hardware characteristics, such as, area utilization, reconfiguration time, and time to communicate configuration bit streams, execution codes, and data. Generally, many of these characteristics are not taken into account by traditional task scheduling systems in distributed grids. In this paper, we present a simulation framework for application task distribution among different nodes of a reconfigurable computing grid. Furthermore, we propose three different task scheduling strategies, namely Optional Closest Match (OCM), Exact Match Priority (EMP), and Sufficient-Area Priority (SAP). The simulation results are presented based on the average scheduling steps required by the scheduler to accommodate each task, the total scheduler workload, and the average waiting time per task. We compare the impacts of the three scheduling strategies on these metrics. In addition, we present a thorough discussion of the results. In particular, the results show that the two key metrics average scheduling steps per task and average waiting time per task are reduced for the EMP and the SAP when compared to the OCM.