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Along with the developments of mobile services, effectively modeling road networks and efficiently indexing and querying network constrained objects has become a challenging problem. In this paper, we first introduce a road network model which captures real-life road networks better than previous models. Then, based on the proposed model, we propose a novel index named the RNG (road network grid) index for accelerating KNN queries and continuous KNN queries over road network constrained data points. In contrast to conventional methods, speed limitations and blocking information of roads are included into the RNG index, which enables the index to support both distance-based and time-based KNN queries and continuous KNN queries. Our work extends previous ones by taking into account more practical scenarios, such as complexities in real-life road networks and time-based KNN queries. Extensive experimental study shows that our methods are efficient in terms of both CPU time and disk I/Os.