# MEC Server Sleep Strategy for Energy Efficient Operation of an MEC System
## 1 Introduction  
The increasing prevalence of high-speed wireless networks, smart mobile devices, and digital services has led to a connected and data-centric society, driving innovation and economic growth across various industries. This digital transformation poses complex challenges such as low-latency data processing, efficient bandwidth utilization, and improved service quality. In response, Multi-Access Edge Computing (MEC) systems have garnered significant attention. MEC systems deploy numerous low-capacity MEC servers (MECSs) at the network edge, utilizing computing and storage resources for low-latency services. This is crucial for applications such as autonomous vehicles, augmented reality, real-time gaming, and healthcare. MEC systems efficiently manage network bandwidth and reduce congestion by processing data at the edge before transmitting it to central data centers. However, the benefit of an MEC system does not come without costs. With the expansion of the service area in MEC systems, there is an associated increase in the required number of MECSs. This escalation in the number of MECS contributes to a higher energy consumption, resulting in an augmented operational expenditure for the MEC system. In addition, networks and data centers are expected to account for 59.8% of the CO2 emissions in the information and communications technology sector by 2030 [1]. Therefore, it is essential to increase the energy efficiency of an MEC system to reduce the operational cost and tackle the environmental conservation problem. An MECS undertakes the reception, processing, and subsequent transmission of results for tasks offloaded from users. Consequently, the energy consumed within an MEC system is categorized into the communication energy and computing energy of MECS. In the task-offloading process, a user device incurs transmission power consumption. Given the typically small size of service results, the downlink transmission power of an MECS is often assumed to be negligible. However, if an MECS cannot handle a service for processing the requested task, task migration to a cloud server or another MECS becomes necessary, constituting a significant portion of the communication energy within an MECS. To mitigate the energy impact of task migration, various service caching methods have been proposed [2; 3; 4]. Given the potential minimization of communication energy using appropriate service caching methods, this paper concentrates on addressing the computing energy consumption issue. Since an MEC system involves complex interactions among diverse elements, a multitude of approaches have been proposed to mitigate computing energy consumption across various facets of MEC systems. For instance, the energy consumed in an MEC system can be reduced via an optimal offloading decision [5], resource management [6], network selection [7], and dynamic voltage and frequency scaling [8]. These methodologies presuppose the active mode for all MECSs within the system, overlooking the temporal and spatial variations in tasks offloaded to each MECS. Generally, the workload imposed on an MEC system is unevenly distributed across MECSs. Thus, when the total system load is below the combined capacity of all MECSs, some MECSs may remain lightly loaded or idle. However, an MECS consumes a substantial amount of energy even in the idle state [9]. To address this, minimizing the total energy consumption of an MEC system involves placing unnecessary MECSs into a sleep state. However, since only active MECSs process loads in an MEC system, the service delay increases with the number of MECSs in the sleep state. Consequently, determining the operation mode of each MECS based on workload distribution becomes crucial for effectively reducing energy consumption while maintaining a reasonable service quality. Various MECS sleep control methods have been proposed to strike a delicate balance between two conflicting performance metrics: the amount of energy consumed and the service latency delivered by an MEC system.