###### Abstract  
To improve the resource efficiency of multi-access edge computing (MEC) systems, it is important to distribute the imposed workload evenly among MEC servers (MECSs). To address this issue, we propose a task redirection method to balance loads among MECSs in a distributed manner. In conventional methods, a congested MECS selects only one MECS to which it redirects tasks. By contrast, the proposed method enables a congested MECS to distribute its tasks to a set of MECSs, the loads of which are lower than that of the congested MECS by determining the number of tasks that it redirects to each selected MECS. We prove that our task redirection method drives a MEC system to a state where the resulting MECS load vector is lexicographically minimal. Through extensive simulation studies, we show that compared with the conventional methods, the proposed method can achieve the smallest load difference between the load of the MECS, the load of which is the highest, and that of the MECS, the load of which is the smallest. By lexicographically minimizing the MECS load vector, the proposed method decreases the average task blocking rate when the task offload rate is high. In addition, we show that the proposed method outperforms the conventional methods in terms of the number of tasks, the delay requirements  
becomes challenging for a central controller to assign tasks to the least-loaded MECS every time a task is offloaded. Distributed approaches were proposed in [7,8]. The method proposed in [7] transfers tasks from highly loaded MECSs to the least-loaded MECS. Similarly, to transfer the tasks offloaded from devices to a MECS, the authors in [8] forced an overloaded MECS to select two MECSs randomly from a set of neighboring MECSs and choose the least-loaded one for offloading. In the case of distributed methods, since all the overloaded MECSs redistribute their tasks to the least-loaded MECS simultaneously, the least-loaded MECS can easily become heavily loaded, which results in a further load unbalance among MECSs. In addition, most approaches do not explicitly consider the delay requirement of a task, nor the amount loads to be redirected to the least-loaded MECS. Load balancing methods based on machine learning were proposed in [9, 10, 11]. After predicting the state of the MEC system in terms of the MECSs loads, the authors proposed methods to balance loads among MECSs. However, the signaling cost of these methods is very high because a central controller must collect an enormous amount of data to analyze the state of the MEC system and transfer the learned model parameters to each MECS. In addition, a relatively long time is required for a controller to learn by analyzing big data, so these methods are not easily applied to short timescales. In [12], game theory was used to resolve the load balancing problem. The cost minimization problem was formulated as a transportation problem, and [PERSON]'s approximation method was used to calculate the optimal solution. However, global information is needed to solve the optimization problem, and the static threshold required to determine the load state of a MECS was not systematically configured. To address these issues, we propose a task redirection method to balance loads among MECSs using a decentralized consensus method [13,14]. We explicitly consider the delay requirement of a task when estimating the MECS load. In our task redirection method, each MECS determines whether to redirect tasks by considering its load state relative to that of the other MECSs. Once MECS \(i\) decides to redirect its tasks; instead of transferring tasks to the least-loaded MECS, \(i\) redistributes its tasks to a set of MECSs whose loads are smaller than its own load. In addition, MECS \(i\) determines the number of tasks to be redirected to each MECS in the set according to the difference between the load of each MECS in the set and its own load. This paper is organized as follows. In Section 2, we introduce a system model and define the load balancing problem in a MEC system.