Abstract. One of the main functions of the traffic navigation systems is to find the optimal route to the destination. In this paper, we propose an iterative Q value updating algorithm, Q method, based on dynamic programming to search the optimal route and its optimal traveling time for a given Origin-Destination (OD) pair of road networks. The Q method uses the traveling time information available at adjacent intersections to search for the optimal route. The Q value is defined as the minimum traveling time to the destination when a vehicle takes the next intersection. When the Q values converge, the optimal route to the destination can be determined by choosing the minimum Q value at each intersection. The Q method gives us the solutions from multiple origins to a single destination. The proposed method is not restricted to find a single solution, but, if there exist multiple optimal routes with the identical traveling time to the destination, the proposed method can find all of it. ...