This paper presents a mathematical model to characterise the performance of a IEEE 802.15.6 Body Area Network (BAN), using a Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) protocol, when a query-based traffic is established. According to the latter, the BAN coordinator periodically triggers nodes, which will immediately start the CSMA/CA protocol, in order to send their data to the coordinator. The model evaluates the packet success probability and the mean delay of packets received from the coordinator. Each node is characterised by a User Priority (UP) value, which affects the Medium Access Control (MAC) protocol parameters. A set of experiments on a real platform has been performed to validate the model. This work can be considered the starting point for a development of a more elaborate mechanism to optimise the UP assignment in order to achieve the performance imposed by the application.