Many of the data sources used in stream query processing are known to exhibit bursty behavior. We focus here on passive network monitoring, an application in which the data rates typically exhibit a large peak-to-average ratio. Provisioning a stream query processor to handle peak rates in such a setting can be prohibitively expensive. In this paper, we propose to solve this problem by provisioning the query processor for typical data rates instead of much higher peak data rates. To enable this strategy, we present mechanisms and policies for managing the tradeoffs between the latency and accuracy of query results when bursts exceed the steady-state capacity of the query processor. We describe the current status of our implementation and present experimental results on a testbed network monitoring application to demonstrate the utility of our approach.