Wireless Body Area Sensor Networks (WBASNs) play a vital role in automation of remote patient monitoring systems (over Internet) for big hospitals, which may ease the responsibilities of the paramedic staff. However, these systems generate huge amount of sensed data, which requires time-bounded services (e.g. latency not more than 250 ms), reliability, data preprocessing, and efficient communication technologies. Internet of Things (IoTs) with the concept of Fog computing is one of the suitable options to enhance the patient monitoring systems. In this context, initially, this paper highlights the requirements of patient monitoring systems, and then proposes and implements a four-Tier architecture of IoTs by integrating WBASNs, fog computing and cloud services over IPv6. Furthermore, the proposed architecture is implemented in small scale as a testbed by using Arduino open-source prototyping platform. After testing, initial results are captured based on latency and reliability. The results show that this architecture fulfills the strict requirements of medical applications by providing reliable communication within the range of 125-250 ms. © 2018 IEEE.