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Upper bound constraints are often set when complex scientific or business processes are modelled as grid workflow specifications. However, many existing processes such as climate modelling or international stock market analysis often have only one end-to-end upper bound constraint. This is not sufficient to control overall temporal correctness as we may not find temporal violations until the last activity. Then, it is too late to take any handling actions. Consequently, the execution results may not be useful and overall cost-effectiveness would be impacted. Therefore, in this paper, we systematically investigate how to set, verify and adjust sub-upper bound constraints within the timeframe of one end-to-end upper bound constraint so that we can control grid workflow execution locally. We develop corresponding setting, verification and adjustment methods and algorithms. The quantitative evaluation demonstrates that with sub-upper bound constraints, we can achieve better cost-effectiveness than only based on one end-to-end upper bound constraint.