In many applications involving continuous data streams, data arrival is bursty and data rate fluctuates over time. Systems that seek to give rapid or realtime query responses in such an environment must be prepared to deal gracefully with bursts in data arrival without compromising system performance. We discuss one strategy for processing bursty streams -- adaptive, load-aware scheduling of query operators to minimize resource consumption during times of peak load. We show that the choice of an operator scheduling strategy can have significant impact on the run-time system memory usage as well as output latency. Our aim is to design a scheduling strategy that minimizes the maximum run-time system memory, while maintaining the output latency within prespecified bounds. We first present Chain scheduling, an operator scheduling strategy for data stream systems that is near-optimal in minimizing run-time memory usage for any collection of singlestream queries involving selections, project...