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This paper investigates the problem of autonomously allocating a large number of independent, equal sized tasks on a distributed heterogeneous grid-like platform, using only local information We propose A-FAST (Autonomous Flow Approach to Scheduling Tasks), an efficient, scalable, dynamic and generic (imposing no restrictions on the topology) protocol for this purpose Motivated by the idea of pressure guiding the flow in fluid networks, A-FAST only uses parameters available locally to a node to guide scheduling decisions Simulations show that the protocol performs well over a variety of networks, averaging more than 99.5% of the optimal performance and outperforms related techniques like RID (Receiver Initiated Diffusion) We also show how a modified use of local information can improve the performance of an unreliable system Preliminary results from implementing A-FAST on a small but real-life distributed system show the performance of our protocol to be near the maximum throughput of the system Such a protocol has the potential to aid the efficient deployment of large, data intensive applications on very large or dynamically changing heterogeneous peer-to-peer computing platforms.