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To maintain quality of service, some heavily trafficked Web sites use multiple servers, which share information through a shared file system or data space. The Andrews file system (AFS) and distributed file system (DFS), for example, can facilitate this sharing. In other sites, each server might have its own independent file system. Although scheduling algorithms for traditional distributed systems do not address the special needs of Web server clusters well, a significant evolution in the computational approach to artificial intelligence and cognitive engineering shows promise for Web request scheduling. Not only is this transformation - from discrete symbolic reasoning to massively parallel and connectionist neural modeling - of compelling scientific interest, but also of considerable practical value. Our novel application of connectionist neural modeling to map Web page requests to Web server caches maximizes hit ratio while load balancing among caches. In particular, we have developed a new learning algorithm for fast Web page allocation on a server using the self-organizing properties of the neural network (NN).