Event processing involves continuous evaluation of queries over streams of events. Response-time optimization is traditionally done over a fixed set of nodes and/or by using metrics measured at query-operator levels. Cloud computing makes it easy to acquire and release computing nodes as required. Leveraging this flexibility, we propose a novel, queueing-theory-based approach for meeting specified response-time targets against fluctuating event arrival rates by drawing only the necessary amount of computing resources from a cloud platform. In the proposed approach, the entire processing engine of a distinct query is modelled as an atomic unit for predicting response times. Several such units hosted on a single node are modelled as a multiple class M/G/1 system. These aspects eliminate intrusive, low-level performance measurements at run-time, and also offer portability and scalability. Using model-based predictions, cloud resources are efficiently used to meet response-time targets. The efficacy of the approach is demonstrated through cloud-based experiments.