Fork-Join Program Response Time on Multiprocessors with Exchangeable Join

A Fork-Join program is one that consist of k ≥ 1 parallel tasks, which is a reasonable model for a large number of computing applications. When the parallel processor have multi-channels, later arrived tasks may finish executions earlier than the early arrived tasks and may join with the finished tasks from different programs. This phenomenon introduce correlation to tasks service times and is called exchangeable join (EJ). The main contribution of this paper is to theoretically investigate the response time of the multiprocessor systems with EJ, which is a novel approach. We analyze two main characters of this kind of system: exchangeable join (EJ) and the capacity constraint (CC) and have proved 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 appropriately constructed based on this analysis and a quick estimation algorithm is proposed. So that the response time of multiprocessors can be fast evaluated. Comparing with extensive simulations, statistical results validate that the relative error of approximation is less than 5%.