We present a GPU-based algorithm for computing discretized distance functions on road networks. As applications, we provide algorithms for computing discrete Order-k Network Voronoi diagrams and for approximately solving k-Nearest Neighbor queries and Aggregate k-Nearest Neighbor queries on road networks. Finally, we present experimental results obtained with the implementation of our algorithms. Categories and Subject Descriptors H.2.8 [Database applications]: Spatial Databases and GIS; H.4.2 [Information Systems Applications]: Decision Support General Terms Algorithms, design, experimentation Keywords Road networks, proximity queries, graphics hardware