The IEEE 802.15.6 standard for wireless body area network (WBAN) defines two contention-based channel access schemes: slotted ALOHA and carrier sense multiple access with collision avoidance (CSMA/CA) using an alternative binary exponential backoff procedure. The standard supports quality of service (QoS) differentiation through user priorities and access phases. In this study, we develop an analytical model for the estimation of normalized throughput and mean frame service time performance of the CSMA/CA protocol as described in the IEEE 802.15.6 standard, employing a Markov chain model under non-saturated heterogeneous traffic scenarios. We also consider a portion of the access phases of the superframe and analyze its impact on the performance of the IEEE 802.15.6 CSMA/CA. Our analysis is validated by accurate computer simulations. Our results show that the IEEE 802.15.6 CSMA/CA employing different access phases degrades the overall system throughput performance and results in higher delay for low priority users.