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Mobile edge caching (MEC) is a promising technique to improve the quality ofservice (QoS) for mobile users (MU) by bringing data to the network edge.However, optimizing the crucial QoS aspects of message freshness and servicepromptness, measured by age of information (AoI) and service delay,respectively, entails a tradeoff due to their competition for shared edgeresources. This paper investigates this tradeoff by formulating their weightedsum minimization as a sequential decision-making problem, incorporatinghigh-dimensional, discrete-valued, and linearly constrained design variables.First, to assess the feasibility of the considered problem, we characterize thecorresponding achievable region by deriving its superset with the ratestability theorem and its subset with a novel stochastic policy, and develop asufficient condition for the existence of solutions. Next, to efficiently solvethis problem, we propose a mixed-order drift-plus-penalty algorithm by jointlyconsidering the linear and quadratic Lyapunov drifts and then optimizing themwith dynamic programming (DP). Finally, by leveraging the Lyapunov optimizationtechnique, we demonstrate that the proposed algorithm achieves an $O(1/V)$versus $O(V)$ tradeoff for the average AoI and average service delay.

AoI-Delay Tradeoff in Mobile Edge Caching: A Mixed-Order Drift-Plus-Penalty Algorithm