The IEEE 802.15.4e standard has four different superframe structures for different applications. Use of a low latency deterministic network (LLDN) superframe for the wireless sensor network is one of them, which can operate in a star topology. In this paper, a new channel access mechanism for IEEE 802.15.4e-based LLDN shared slots is proposed, and analytical models are designed based on this channel access mechanism. A prediction model is designed to estimate the possible number of retransmission slots based on the number of failed transmissions. Performance analysis in terms of data transmission reliability, delay, throughput and energy consumption are provided based on our proposed designs. Our designs are validated for simulation and analytical results, and it is observed that the simulation results well match with the analytical ones. Besides, our designs are compared with the IEEE 802.15.4 MAC mechanism, and it is shown that ours outperforms in terms of throughput, energy consumption, delay and reliability.