Fork-Join program response time on multiprocessors with exchangeable join

The Fork-Join program consisting of K parallel tasks is a useful model for a large number of computing applications. When the parallel processor has multi-channels, later tasks may finish execution earlier than their earlier tasks and may join with tasks from other programs. This phenomenon is called exchangeable join (EJ), which introduces correlation to the task’s service time. In this work, we investigate the response time of multiprocessor systems with EJ with a new approach. We analyze two aspects of this kind of systems: exchangeable join (EJ) and the capacity constraint (CC). We prove that the system response time can be effectively reduced by EJ, while the reduced amount is constrained by the capacity of the multiprocessor. An upper bound model is constructed based on this analysis and a quick estimation algorithm is proposed. The approximation formula is verified by extensive simulation results, which show that the relative error of approximation is less than 5%.