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Managing the performance of multiple-tiered Web sites under high client loads is a critical problem with the advent of dynamic content and database-driven servers on the Internet. This paper presents a control-theoretic approach for admission control in multitiered Web sites that both prevents overload and enforces absolute client response times, while still maintaining high throughput under load. We use classical control theoretic techniques to design a proportional integral (PI) controller for admission control of client HTTP requests. In addition, we present a processor-sharing model that is used to make the controller self-tuning, so that no parameter setting is required beyond a target response time. Our controller is implemented as a proxy, called Yaksha, which operates by taking simple external measurements of the client response times. Our design is noninvasive and requires minimal operator intervention. We evaluate our techniques experimentally using a 3-tiered dynamic content Web site as a testbed. Using the industry standard TPC-W client workload generator, we study the performance of the PI admission controller with extensive experiments. We show that the controller effectively bounds the response times of requests for dynamic content while still maintaining high throughput levels, even when the client request rate is many times that of the server's maximum processing rate. We demonstrate the effectiveness of our self-tuning mechanism, showing that it responds and adapts smoothly to changes in the workload.