Application areas that utilize the concept of IoT can be broadened to healthcare or remote monitoring areas. In this paper, a remote monitoring system for patients at home in IoT environments is proposed, constructed, and evaluated through several experiments. To make it operable in IoT environments, a protocol conversion scheme between ISO/IEEE 11073 protocol and oneM2M protocol, and a Multiclass Q-learning scheduling algorithm based on the urgency of biomedical data delivery to medical staff are proposed. In addition, for the sake of patients' privacy, two security schemes are proposed-the separate storage scheme of data in parts and the Buddy-ACK authorization scheme. The experiment on the constructed system showed that the system worked well and the Multiclass Q-learning scheduling algorithm performs better than the Multiclass Based Dynamic Priority scheduling algorithm. We also found that the throughputs of the Multiclass Q-learning scheduling algorithm increase almost linearly as the measurement time increases, whereas the throughputs of the Multiclass Based Dynamic Priority algorithm increase with decreases in the increasing ratio.