Wireless Body Area Network (WBAN) has been an active area of research over the past few years due to its tremendous benefits particularly related to healthcare systems. Through WBAN, the physicians can get real time updates for a long period of time in an inexpensive way about their patients who are suffering from different kinds of chronic diseases such as diabetes, asthma and myocardial infarction etc. A number of issues need to be addressed in the area of WBAN. There is a very strong need to develop scalable and low power MAC protocols. Further, novel and sophisticated queuing models are also needed to develop in order to provide guaranteed QoS to different classes of traffic generating from different types of events in WBAN. This paper focuses to analyze a three queues priority model for low power WBAN, which enables to provide guaranteed QoS to different types of traffic generated from different events. We extract closed form expressions of various QoS parameters such as queue length, queuing delay, throughput and packet loss rate. We also simulate the behaviour of traffic in WBAN to further evaluate the proposed analytical framework.