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Autoscaling methods are employed to ensure the scalability of cloud-hosted applications. The public-facing applications are prone to receive sudden workload bursts, and the existing autoscaling methods do not handle the bursty workloads gracefully. It is challenging to detect the burst online from the incoming dynamic workload traffic, and then identifying appropriate resources to address the burst without overprovisioning is even harder. In this paper, we address this challenge by investigating the appropriate method for online burst detection and then proposed a novel predictive autoscaling method to use burst detection for satisfying specific response time requirements. We compared the proposed method with multiple state-of-the-art baseline autoscaling methods under multiple realistic and synthetic bursty workloads for a benchmark application. Our experimental results show a 60.8% average decrease in response time violations as compared to the baseline method.