Moving nearest neighbor queries in road networks have been studied extensively in recent years. However, at present there is still a lack of algorithms for moving queries in a directed road networks. In this thesis, we introduce a new algorithm called the Directed Safe Exit Algorithm (DSEA), which can efficiently compute the safe exit points of a moving nearest neighbor (NN) query on directed road networks where each road segment has a particular orientation. The safe region of a query is an area where the query result remains unchanged, provided that the query remains inside the safe region. At each safe exit point, the safe region of a query and its non-safe region meet so that a set of safe exit points represents the border of the safe region. Before reaching a safe exit point, the client (query object) does not have to request the server to re-evaluate the query. This significantly reduce the server processing cost and the communication costs between the server and moving clients. Our experimental results demonstrate that DSEA significantly outperforms a conventional solution in terms of both computational and communication costs.