Many services rely on the Internet to provide their customers with immediate access to information. To provide a stable service to a large number of customers, a service provider needs to monitor demand fluctuations and adjust the number and the location of replica servers around the world. Unfortunately, Flash crowds make it quite difficult to determine good number and locations of replica servers because they must be repositioned very quickly to respond to rapidly changing demands. We are developing ExaPeer, an infrastructure for dynamically repositioning replica servers on the Internet on the basis of demand fluctuations. In this paper we introduce ExaPeer Server Reposition (EPSR), a mechanism that quickly finds appropriate number and locations of replica servers. EPSR is designed to be lightweight and responsive to Flash crowds. EPSR enables us to position replica servers so that no server becomes overloaded. Even though no dedicated server collects global information such as the distribution of clients or the load of all servers over the Internet, the peer-to-peer approach enables EPSR to find number and locations of replica servers quickly enough to respond to flash crowds. Simulation results demonstrate that EPSR locates high-demand areas, estimates their scale correctly and determines appropriate number and locations of replica servers even if the demand for a service increases/decreases rapidly.