## 3 Proposed Algorithm  
In this paper, we aim to maximize task throughput and minimize processing delay by considering the occurrence of tasks that are difficult to predict at train stations with dense user traffic and the characteristics of HSTs that are different from existing vehicles. To achieve this, we need to determine the optimal ratio when tasks are processed by multiple MECSs. The optimized partitioning ratio contributes to the efficient processing of tasks and plays an important role in improving the performance of the entire system. In the dynamic HSR environment, the number of HSTs and the passenger density aboard each HST vary over time. Passenger density is closely related to the task size, as a higher number of passengers increases the likelihood of task generation, thereby leading to larger task sizes that need to be processed by the MEC servers (MECSs). When task generation is minimal, a single MECS can handle the task without being overloaded. However, during peak passenger density, efficient task partitioning becomes crucial to prevent MECS overload and ensure QoS. Additionally, the dynamic changes in the number of HSTs influence the task partitioning decisions among the MECSs. For instance, if an HST allocates a significant proportion of its tasks to a specific MECS, and another HST similarly allocates a large proportion to the same MECS, this increases the likelihood of overloading that MECS. Furthermore, MECSs do not only process tasks received from HSTs, but the overhead of MECSs must also be considered. Therefore, determining the optimal task partitioning ratio is critical for achieving load balancing across MECSs, reducing both overloaded and underutilized MECSs. This dynamic and adaptive partitioning mechanism ensures efficient resource utilization and maintains QoS in the constantly changing HSR environment. The proposed algorithm optimizes the task partitioning ratio in HSR environments through a two-step process. In the first step, a set of serving MECSs, \(\mathcal{K}=\{1,\ldots,k,\ldots,K\}\subseteq\mathcal{M}\), is selected to support the divided subtasks. This selection is based on the MECS selection probability \((P_{load})\), which is defined as follows for each MECS \(m\in\mathcal{M}\):  
\[P_{load}=1-\frac{queue_{m}(t)}{\sum_{m=1}^{M}queue_{m}(t)}, \tag{9}\]  
where \(queue_{m}(t)\) represents the load of MECS \(m\) at time \(t\), such as the size of its current task queue. This probability ensures that MECSs with higher loads have a lower likelihood of being selected, thereby balancing the load across the available MECSs and reducing the risk of overloading any specific MECS. By selecting a subset of serving MECSs, rather than considering the entire set of MECSs for each decision, the algorithm effectively reduces the action space for decision-making. This dimensionality reduction simplifies the optimization process while maintaining an efficient task distribution among MECSs. In the second step, the task partitioning ratio is dynamically determined for the \(k\) selected serving MECSs by utilizing the TD3 algorithm. The problem is that the existing static partitioning research has limitations in producing optimal results due to the dynamic environment that cannot be predicted at every time slot and the large number of tasks generated by the dense users. In such a complex environment, the task partitioning ratio becomes more important, so we intend to determine the optimal partitioning ratio through deep reinforcement learning (DRL). First of all, among the DRL methods, Deep Q-Network(DQN) [22] and Deep Deterministic Policy Gradient (DDPG) [23] are widely used. However, DQN is not suitable for continuous action decisions such as task partitioning ratio decisions. And DDPG is suitable for continuous action decisions, but it can cause unstable learning due to the overestimation bias and the accumulating error problem in the TD update process. Therefore, TD3, which has improved this, was selected. There are three main features to solve the aforementioned problems.