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With the recent advent of cloud computing technologies, a growing number of content distribution applications are contemplating a switch to cloud-based services, for better scalability and lower cost. Two key tasks are involved for such a move: to migrate the contents to cloud storage, and to distribute the Web service load to cloud-based Web services. The main issue is to best utilize the cloud as well as the application provider's existing private cloud, to serve volatile requests with service response time guarantee at all times, while incurring the minimum operational cost. While it may not be too difficult to design a simple heuristic, proposing one with guaranteed cost optimality over a long run of the system constitutes an intimidating challenge. Employing Lyapunov optimization techniques, we design a dynamic control algorithm to optimally place contents and dispatch requests in a hybrid cloud infrastructure …