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It has long been recognized that multi-stream operators, such as union and join, often have to wait idly in a temporarily blocked state, as a result of skews between the timestamps of their input streams. It has been shown that the injection of heartbeat information through punctuation tuples can alleviate this problem. In this paper, we propose and investigate more effective solutions that use timestamps generated on-demand to reactivate idle-waiting operators. We thus introduce a simple execution model that efficiently supports on-demand punctuation. Experiments show that response time and memory usage are reduced substantially by this approach.