# Proactive Service Caching in a MEC System by Using Spatio-Temporal Correlation among MEC Servers
## 2 Related Works  
### Caching in a MEC System  
Various cache management methods have been proposed for a MEC system. In [19; 20], a game-theoretic approach is taken for making a caching decision. After modeling the interaction between a MECS and wireless devices as a two-stage Stackelberg game under incomplete information, the authors in [19] devise two strategies for the game. The first strategy is used for a MECS to make the caching and the price decision. The second strategy is used for a wireless device to make a task offloading decision. A stochastic \begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Meaning** \\ \hline \(\mathcal{M}=\{1,\dots M\}\) & A set of MECS in a MEC system \\ \(\mathcal{K}=\{1,\dots K\}\) & A set of services provided by a MEC system \\ \(\eta_{m}\) & Service cache size of MECS \(m\) \\ \(a_{m,k}(t)\) & 1: a service \(k\) is cached at MECS \(m\) during a time slot \(t\), 0: otherwise. \\ \(A_{M\times K}(t)\) & Service cache state of a MEC system during a time slot \(t\) \\ \(S_{m}(t)\) & A set of services cached at MECS \(m\) during a time slot \(t\) \\ \(U_{m}(t)\) & A set of users in the service area of MECS \(m\) during a time slot \(t\) \\ \(b_{m,u,k}(t)\) & 1: a service \(k\) requested by user \(u\) is at MECS \(m\) during a time slot \(t\). 0: otherwise \\ \(f_{m,k}(t)\) & popularity of a service \(k\) in MECS \(m\) during a time slot \(t\) \\ \(F_{M\times K}(t)\) & service popularity matrix of a MEC system during a time slot \(t\) \\ \(w_{a}\) & the number of recent past heatmap images used for prediction \\ \(b_{m,k}(t)\) & the number of times MECS \(m\) receives the request of service \(k\) during a time slot \(t\) \\ \(Z_{m}(t)\) & the set of \(b_{m,k}(t)\) at a MECS \(m\) (\(\forall k\in\mathcal{K}\)) \\ \(v_{m,k}(t)\) & \(f_{m,k}(t)\) normalized by \(f_{m}^{M}(t)=max_{k\in\mathcal{K}}(f_{m,k}(t))\) \\ \(\Omega(t)\) & a heatmap image of a MEC system at the end of a time slot \(t\) \\ \(\hat{\Omega}(t)\) & predicted heatmap image of a MEC system at the start of a time slot \(t\) \\ \(\delta_{m,k}(t)\) & popularity prediction error for a service \(k\) at MECS \(m\) during a time slot \(t\) \\ \(a_{m}(t)\) & service cache similarity degree at MECS \(m\) during a time slot \(t\) \\ \(\rho_{m}(t)\) & relative service cache hit rate at MECS \(m\) during a time slot \(t\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Notations used. differential game is used in [20] to formulate a dynamic cache control problem. Since the computational complexity of the problem is huge, both the mean-field game theory and the stochastic-geometry are used to transform the original problem into a more tractable form. Then, authors propose an iterative algorithm for optimal caching control. However, these game-theoretic methods require information exchange among the players. Thus, the control overhead increases in proportion to the number of devices and the number of MECSs. In addition, they require an iterative process to reach an equilibrium state. Therefore, they cannot make a decision until the iterative process converges nor adapt quickly to topology changes. In [21], a service cache placement problem and a task offloading problem are jointly investigated. The joint problem is formulated as an average service response time minimization problem with a long-term energy consumption constraint. To resolve the problem without unknown future information, an online algorithm is devised by using the Lyapunov optimization framework and deep reinforcement learning (DRL). DRL-based methods are also proposed in [22; 23]. The authors in [22] propose a cooperative video caching method for a MEC system by combining the knowledge graph (KG) and DRL. The KG is used to determine a set of candidate videos by inferrinIn [23], a model-free reinforcement learning algorithm called RL-Cache is proposed to decide whether or not to accept a requested object into the content distribution network's cache.