A web geographical information system is a typical service-intensive application. Tile prefetching and cache replacement can improve cache hit ratios by proactively fetching tiles from storage and replacing the appropriate tiles from the high-speed cache buffer without waiting for a client's requests, which reduces disk latency and improves system access performance. Most popular prefetching strategies consider only the relative tile popularities to predict which tile should be prefetched or consider only a single individual user's access behavior to determine which neighbor tiles need to be prefetched. Some studies show that comprehensively considering all users' access behaviors and all tiles' relationships in the prediction process can achieve more significant improvements. Thus, this work proposes a new global user-driven model for tile prefetching and cache replacement. First, based on all users' access behaviors, a type of expression method for tile correlation is designed and implemented. Then, a conditional prefetching probability can be computed based on the proposed correlation expression mode. Thus, some tiles to be prefetched can be found by computing and comparing the conditional prefetching probability from the uncached tiles set and, similarly, some replacement tiles can be found in the cache buffer according to multi-step prefetching. Finally, some experiments are provided comparing the proposed model with other global user-driven models, other single user-driven models, and other client-side prefetching strategies. The results show that the proposed model can achieve a prefetching hit rate in approximately 10.6% ~ 110.5% higher than the compared methods.