In this work a permutation flow-shop based model for grid computing systems along with some novel theoretical results is presented. The aim is characterizing a suitable policy for grid brokers when dealing with the balance between upcoming requests and available resources. Provided that even the simple scheduling of serial jobs on a single grid node represents a significant deal of research topics, this is a really challenging task. Some cost-functions to evaluate makespan are presented for the well-known case referring to two machines with no intermediate buffer. Some specific solutions for heavy-constrained situations are also provided. A sample application of the found theorem and lemmas is extensively described in the text. It helps understand how effective certain scheduling algorithms may be, particularly in constrained conditions. Further works will be aimed at transferring these results into new grid scheduler implementing rules.
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