Recently, location service using Bluetooth Low-Energy (BLE) beacon is gaining popularity. There also exist researches that estimate the route of the user from the location estimation results, visualize, and analyze it. In the conventional route estimation method based on the BLE beacon, after estimating the all locations from the radio field strength of the BLE, the route is estimated from the sequence of the estimated locations. Therefore, one of the causes of deterioration in accuracy could be the fact that the estimation was repeated twice. Therefore, in this paper, we propose a novel estimation method of the user's route and stay using BLE beacons. Specifically, we apply the idea of global map matching, used in the field of GPS, to route estimation based on BLE beacons. Thus, the global optimum route in beacon network can be estimated from the radio field intensities of the BLE beacon directly. We associate a beacon network with path network to estimate the route and stay of users. We installed approximately 1,600 BLE beacon transmitters in all the classrooms and corridors of Nagoya Institute of Technology, and confirmed the effectiveness of the proposed method by experiments.