## 2 Related Works  
Several research works have demonstrated that the strategic positioning of MECSs can optimize system performance. Through efficient load balancing across MECSs, these approaches successfully reduce user access latency while achieving improved energy efficiency. In [17], authors propose a MECS placement technique focused on optimizing global latency and load balancing. Their approach divides the service area of the MEC system into zones and employs the coral reef optimization algorithm to determine optimal local resource placement for each zone. Subsequently, they utilize DQN and Markov game theory to establish global resource placement, thereby improving both objectives while enhancing MECS energy efficiency. The authors in [18] introduce a method for predicting optimal MECS locations by considering urban user mobility and spatial patterns to ensure energy efficiency while minimizing outages. The authors develop CrowdEdgeSim, a simulator capable of dynamically modeling urban mobility, networks, and computing resources simultaneously. This development is based on their proposed urban mobility model, which utilized GPT (Google Popular Times) data. However, such static MECS placement schemes face limitations in adapting to emerging services or evolving user characteristics, which makes it challenging for them to optimize long-term energy efficiency of the system. In contrast, MECS sleep control techniques offer a more efficient approach to improving energy efficiency, as they can adaptively respond to changes in user behavior patterns without requiring physical modifications to the MEC system infrastructure. To address the challenge of energy consumption in MEC systems, numerous demand response techniques have been proposed in the literature, which primarily focus on efficient workload distribution across multiple MECSs [19]. The authors in [20] propose a novel mechanism that optimizes energy cost by leveraging geographical variations in electricity prices at server locations. They demonstrate that operational costs can be minimized effectively by distributing workload strategically. In [21], the authors introduce an approach incorporating energy storage systems and present a comprehensive solution for mitigating peak load demands in MEC infrastructures. This integration of energy storage capabilities provides enhanced flexibility in managing power consumption patterns and reducing overall system stress during high-demand periods. A framework for enhancing system energy efficiency through a sophisticated two-phase approach is presented in [22]. The first phase involves developing a controllable load model for MECS clusters based on task migration principles. In the second phase, they implement dynamic cluster load control through strategic MECS and cloud server collaboration. However, these methodologies maintain all MECSs in an active state while managing workload distribution. This continuous active state requirement inherently constrains the potential for energy optimization. Consequently, the achievable energy savings are lower compared with MECS operational state management techniques that employ strategic server deactivation protocols for redundant or underutilized units [23]. In [24; 25], authors propose methods that place as many servers as possible into an idle state where they have no tasks to process and minimize the energy consumption of these idle servers through the use of specialized hardware. However, as servers still consume a considerable amount of energy even in the idle state, further improvement in the system energy efficiency can be achieved by putting unnecessary servers into a sleep state by turning them off [26]. Similar to mobile device power management techniques that implement sleep states during periods of inactivity, various methodologies have been proposed to dynamically determine the operational states (i.e., sleep or active states) of MECSs.