Mathematical Foundation for Adaptive Superframe Configuration in Hybrid MAC Protocols for Wireless Robotic Networks

The paper proposes a mathematical approach to adaptive superframe reconfiguration in hybrid MAC protocols for wireless mobile robotic networks. The considered network uses a hybrid access mechanism that combines contention-based and contention-free transmission periods within a superframe. The proposed approach is based on a probabilistic model of transitions between three traffic-priority states: low, medium, and high. A system of differential equations is developed to describe the state transitions, and analytical expressions for the stationary probabilities of the traffic-priority states are obtained. The probability of the high-priority traffic state is proposed as a decision criterion for adaptive adjustment of the relative durations of superframe periods. The influence of transition intensities on the state probabilities is analyzed, including their individual and combined effects. Within the examined range, the proposed probabilistic criterion is more sensitive to changes in the selected transition intensities at their lower values and tends toward saturation as these intensities increase. The proposed mathematical model provides a theoretical basis for adaptive resource allocation and superframe configuration in wireless robotic networks with dynamically changing traffic conditions.