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Denial of Service (DoS) attacks overwhelm online services, preventing legitimate users from accessing a service, often with impact on revenue or consumer trust. Approaches exist to filter network-level attacks, but application level attacks are harder to detect at the firewall. Filtering at this level can be computationally expensive and difficult to scale, while still producing false positives that block legitimate users. This paper presents a model-based adaptive architecture and algorithm for detecting DoS attacks at the web application level and mitigating them. Using a performance model to predict the impact of arriving requests, a decision engine adaptively generates rules for filtering traffic and sending suspicious traffic for further review, which may ultimately result in dropping the request or presenting the end user with a CAPTCHA to verify they are a legitimate user. Experiments performed on a scalable implementation demonstrate effective mitigation of attacks launched using a real-world DoS attack tool.