Because it is difficult to find empty space in a developed city to accommodate more transportation infrastructures, the development of an effective navigation system is a low cost option for mitigating traffic jam. Regarding a future world where automated driving technologies have become mature and most vehicles follow the pre-scheduled route suggested by a navigation system, it is likely to predict the traffic jam accurately if the navigation system can know the pre-scheduled route of each vehicle. Recently, a navigation algorithm is presented for automated driving vehicles with the assumption that all the navigating query requests are processed by a single system. However, the aforementioned algorithm does not consider any kind of uncertainty originating from accidents and destination change. To get close to the real world, we propose a navigation algorithm with near-future evaluation capability that also allows some kinds of uncertainties. We compare our algorithm with a dynamic-update based conventional navigation algorithm without near-future evaluation capability. We download some metropolitan maps from OpenStreetMap and utilize the data of traffic flow from official statistics to randomly generate many sets queries. Experimental results show that the total cruising time is improved for each case.