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Existing off-line schedulability analysis for real-time systems can only handle periodic or sporadic tasks with known minimum inter-arrival times. Modeling sporadic tasks with fixed minimum inter-arrival times is a poor approximation for systems in which tasks arrive in bursts, but have longer intervals between the bursts. In such cases, schedulability analysis based on the existing sporadic task model is pessimistic and seriously overestimates the task's time demand. In this paper, we propose a generalized sporadic task model that characterizes arrival times more precisely than the traditional sporadic task model, and we develop a corresponding schedulability analysis that computes tighter bounds on worst-case response times. Experimental results show that when arrival time jitter increases, the new analysis more effectively guarantees schedulability of sporadic tasks.