This paper proposes GRIDTS, a grid infrastructure in which the resources select the tasks they execute, on the contrary to traditional infrastructures where schedulers find resources for the tasks. This solution allows scheduling decisions to be made with up-to-date information about the resources, which is difficult in the traditional infrastructures. Moreover, GRIDTS provides fault-tolerant scheduling by combining a set of fault tolerance techniques to cope with crash faults in components of the system. The solution is mainly based a tuple space, which supports the scheduling and also provides support for the fault tolerance mechanisms.