Wireless body area network (WBAN) is a network of wearable or implanted sensors around or inside human body. In 2012, the IEEE 802.15 Working Group developed a new communication standard IEEE 802.15.6 specifically for WBAN. The primary medium access control technique defined in this standard for narrow-band communication is slotted CSMA/CA mechanism supporting differentiated QoS service. To understand the intrinsic nature of this mechanism, the backoff procedure under saturation condition is modeled by Markov chain so that throughput, successful packet delivery rate, and delay are analyzed. Simulation results confirm the accuracy of the model analysis. Both analysis and simulation results show that this standard provides differentiated service for different priorities, however, also indicates that under saturation condition the medium is mostly preempted by the highest priority while starving other priorities.