The IEEE 802.15.4 standard has been introduced for low latency and low energy consumption in wireless sensor networks. To better support the requirements of industrial applications, where the use of this standard is limited, the low latency deterministic network (LLDN) mechanism of the IEEE 802.15.4e amendment has been proposed. In this paper, we develop a three dimensional Markov chain model for the IEEE 802.15.4e LLDN mechanism. Then, we estimate the stationary probability distribution of this chain in order to derive theoretical expressions of some performance metrics, as the reliability, energy consumption, throughput, delay and jitter. After that, we conduct a comparative study between the IEEE 802.15.4e LLDN and the IEEE 802.15.4 slotted carrier sense multiple access with collision avoidance (CSMA/CA). Numerical results show that the deterministic behavior of the LLDN mechanism significantly reduces the collision probability providing best performances in terms of reliability, energy consumption, throughput and delay compared to the IEEE 802.15.4 slotted CSMA/CA. Finally, the accuracy of our theoretical analysis is validated by Monte Carlo simulations