In recent years, various researches on covering the shadow areas have been conducted around the world through moving base stations using unmanned aerial vehicles (UAVs). Most recently, communication using UAVs has been in the spotlight for military and civilian users because of its low cost and variety usage. In particular, studies related to aerial base station using UAVs are being actively conducted because of the convenience of operation in local areas such as city or mountainous areas, where communications are unavailable. Although most studies have focused on optimal UAV localization to provide efficient communications for outdoor users, supporting indoor users is also of great importance. Especially, the importance of indoor users increase even more in disaster situation. In a disaster situation, it is important to connect many users at early stage by receiving rescue signals from all users at least once. In addition, it is important to receive a lot of continuously requested rescue status signals of many users to recognize and send the current status to rescue team. Therefore, this thesis proposes optimal trajectory frame-work using Lyapunov optimization for receiving continuous rescue signals of many users. Moreover, we consider initial time for connecting all users. First, the additional information in acknowledgement (ACK) packet is considered for initial user connection in disaster environment. This method guarantee that users are served at least once that all the most important in a disaster environment. Second, the Lyapunov optimization-based UAV trajectory is designed based on the characteristics of trade-off constants. In performance evalution, two building types were considered: standard- and factory-type buildings. In conclusion, the performance evaluation results prove that the proposed Lyapunov optimization-based UAV trajectory achieves desired performance based on the characteristics of trade-off constants.