The advancement in the utilization and technologies of the Internet has led to the rapid growth of grid computing; and the perpetuating demand for grid computing resources calls for an incentive-compatible solution to the imminent QoS problem. This paper examines the optimal service priority selection problem that a grid computing network user will confront. We model grid services for a multi-subtask request as a prioritized PERT graph and prove that the localized conditional critical path, which is based on the cost-minimizing priority selection for each node, sets the lower bound for the length of cost-effective critical path that commits the optimal solution. We also propose a heuristic algorithm for relaxing the nodes on the non-critical paths with respect to a given critical path.