Recently, there have been several promising techniques developed for schedulability analysis and response time analysis for multiprocessor systems based on over-approximation. This paper contains two contributions. First, to improve the analysis precision, we apply Baruah’s window analysis framework [6] to response time analysis for sporadic tasks on multiprocessor systems where the deadlines of tasks are within their periods. The crucial observation is that for global fixed priority scheduling, a response time bound of each task can be efficiently estimated by fixed-point computation without enumerating all the busy window sizes as in [6] for schedulability analysis. The technique is proven to dominate theoretically state-of-the-art techniques for response time analysis for multiprocessor systems. Our experiments also show that the technique results in significant performance improvement compared with several existing techniques for multiprocessor schedulability analysis. As th...