Summary form only given. Data stream management systems are being developed to process continuous queries over multiple data streams. These continuous queries are typically used for monitoring purposes where the detection of an event might trigger a sequence of actions or the execution of a set of specified tasks. Such events are identified by tuples produced by a query and hence, it is important to produce the available portions of a query result as early as possible. A core element for improving the interactive performance of a continuous query is the operator scheduler. An operator scheduler is particularly important when the processing requirements and the productivity of different streams are highly skewed. The need for an operator scheduler becomes even more crucial when tuples from different streams arrive asynchronously. To meet these needs, we are proposing a preemptive rate-based scheduling policy that handles the asynchronous nature of tuple arrival and the heterogeneity in the query plan. Experimental results show the significant improvements provided by our proposed policy.