Aging and Delay Analysis Based on Lyapunov Optimization and Martingale Theory

The age of information (AoI) is a key performance metric for data freshness in real-time systems, measuring the time elapsed between status updates received at a remote destination. This paper addresses the analysis of both the AoI and the delay for a system demanding timely status updates, consisting of an internet of things (IoT) community, and a multi-core edge computing node (EN). The IoT devices perform channel contention according to a slotted aloha non-orthogonal multiple access scheme with two transmission power levels to access the EN. The objective of the paper is the dynamic selection of both the EN computation capabilities and the suitable access probability for the two power levels, aiming at maximizing the time-average system utility, while guaranteeing the queues stability. The device end-to-end delay is analyzed by resorting to the martingale theoretical approximation under the condition that the Lyapunov optimization framework is performed on a time slot basis, hence leading to a novel instantaneous mixed integer problem formulation. Furthermore, the generalized benders decomposition method is employed to provide a suboptimal solution for the formulated problem. Finally, the accuracy of the proposed framework is validated by comparing the obtained analytical predictions with simulation results.