Background: The privacy enabled IPv6 addressing mechanism ensures the privacy of the node's identification in the communication messages. It makes it difficult for adversaries to track nodes and link any activities with the node's IP or the MAC address. Scalability of the privacy enabled IPv6 addressing scheme for 6LoWPAN may be affected due to underlying MAC layer mechanisms.Objective: Hence, this study aims to explore such an impact. Methods: Addressing scheme is implemented in the Contiki operating system which uses duty cycling at the MAC layer along with the CSMA channel access mechanism. ContikiMAC and CXMAC are widely used duty cycling protocols in Contiki. An analytical study is presented in this paper, which analyses the IPv6 address configuration delay with ContikiMAC and CXMAC. Simulation is performed to corroborate the presented analytical model. The address configuration latency limits the scalability of the network. Hence, this paper studies the impact of duty cycling of the nodes on the address configuration latency and estimates the size of a single hop PAN. Results & Conclusion: It is observed that the ContikiMAC duty cycling protocol can achieve better performance compared to the CXMAC protocol in terms of address configuration latency. In order to make up for the delay due to duty cycling, the network can be divided into multiple PANs of smaller sizes where the addressing process runs simultaneously.