AoI-Delay Tradeoff in Mobile Edge Caching: A Lyapunov Optimization-Based Method

Mobile edge caching (MEC) is a promising technique to improve the quality of service (QoS) for mobile users (MU) by bringing data to the network edge. However, optimizing the crucial QoS aspects of message freshness and service promptness, measured by age of information (AoI) and service delay, respectively, entails a tradeoff due to their competition for shared edge resources. This article investigates this tradeoff by formulating their weighted sum minimization as a sequential decision-making problem, incorporating high-dimensional, discrete-valued, and linearly constrained design variables. First, to assess the feasibility of the considered problem, we characterize the corresponding achievable region by deriving its superset with the rate stability theorem and its subset with a novel stochastic policy, and develop a sufficient condition for the existence of solutions. Next, to efficiently solve this problem, we propose a mixed-order drift-plus-penalty algorithm by jointly considering the linear and quadratic Lyapunov drifts and then optimizing them with dynamic programming (DP). Finally, by leveraging the Lyapunov optimization technique, we demonstrate that the proposed algorithm achieves an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(1/V)$ </tex-math></inline-formula> versus <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(V)$ </tex-math></inline-formula> tradeoff for the average AoI and average service delay.