AbstractFor many applications, it is important to evaluate trigger conditions on streaming time series. In a resource constrained environment, users' needs should ultimately decide how the evaluation system balances the competing factors such as evaluation speed, result precision, and load shedding level. This paper presents a basic framework for evaluation algorithms that takes user-specified quality requirements into consideration. Three optimization algorithms, each under a different set of user-defined probabilistic quality requirements, are provided in the framework: (1) minimize the response time given accuracy requirements and without load shedding; (2) minimize the load shedding given a response time limit and accuracy requirements; and (3) minimize one type of accuracy errors given a response time limit and without load shedding. Experiments show that these optimization algorithms effectively achieve their optimization goals while satisfying the corresponding quality requirements.