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Mobile Edge Computing (MEC) is a well-known network architecture that extends cloud computing to the network edge. Compared with cloud computing, Network Function Virtualization (NFV) can provide flexible services in MEC for mobile users. Virtual Network Functions (VNFs) have emerged as software-based hardware middleboxes by NFV technology to host real-time applications. Basically, the combination of multiple VNF instances is defined as a Service Function Chain (SFC), which can provide dynamic service requirements in the MEC. Despite the rapid growth of MEC and the widespread support of service providers for SFC, many issues are still challenging and need to be addressed. In MEC scenarios with limited resources, the effective placement of SFCs with the aim of resource efficiency remains a challenging problem. Motivated by the scalability shortcomings of existing schemes to solve dynamic placement of SFCs, we propose Deep Reinforcement Learning (DRL)-based approaches to solve this problem, i.e., Asynchronous Advantage Actor-Critic (A3C). The proposed scheme is based on the reuse of initialized VNFs to improve the Quality of Service (QoS), which is developed with the aim of maximizing the long-term cumulative reward. In addition, a parallel processing approach of SFCs is included in the proposed scheme, which can split the traffic in each flow into sub-flows. This shares the processing load by instantiating duplicate instances of each VNF type in the SFC. The simulation results guarantee the efficiency of the proposed scheme and improves the average performance between 6% and 24% compared to the state-of-the-art clustering methods.