## 1 Introduction  
With the tremendous growth of the Internet of Things (IoTs), massive amounts of mobile devices (MDs), such as smart devices and virtual reality (VR) glasses, connect to networks and generate large amounts of data on communications networks. Moreover, many new IoT applications, such as smart healthcare, surveillance, real-time online gaming, and augmented/VR, require increased energy efficiency and higher computing capacity [1; 2]; however, MDs often have limited computing power and low-capacity batteries, with these limitations representing obstacles for the network deployment and the emergence of new applications and services. To address this, multi-access edge computing (MEC) represents a promising solution for enhancing the computing capabilities and limited battery power of MDs. Computation offloading to MEC servers allows them to process the computational tasks of MDs at the edge of mobile cellular networks through wireless links, which addresses latency problems between cloud servers and MDs, as well as MD-specific limitations in computational power and storage. MEC brings cloud resources (e.g., MEC servers) to the network edges, thereby enabling heavy computing tasks to be performed close to the end user [2; 3; 4; 5]. However, due to the resource limitation of the MEC server, computation offloading remains challenging. In particular, the rapid increase in compute-intensive tasks (such as face recognition, augmented reality, and autonomous driving) from devices will cause server resource bottlenecks of the MEC server and significantly affect task execution latency. Therefore, offloading calculation strategies and resource allocation optimization (e.g., computing resources at MEC server and transmit power) are needed to improve the performance of computation offloading. Exponential increases in data traffic have been addressed through the use of heterogeneous networks (HetNets) comprising homogeneous cell macro-base stations (MBSs) with high transmission power overlaid onto low-power small cell base stations (SBSs) (e.g., femto-cells, pico-cells, and micro-cells) to meet data-rate requirements for next-generation networks [6; 7; 8]. Therefore, integrating MEC into 5G networks in order to increase network performance, to reduce MD-related power consumption, and to utilize macro and small cells represents a research interest in academia and industry. Recent studies have focused on computation offloading in 5G networks [5], with other research focusing on single-tier MEC servers used in heterogeneous scenarios [9; 10; 11; 12; 13; 14; 15]; however, achieving effective offloading decisions related to computation-completion time and energy consumption in a multi-tier MEC server remains an optimization problem that attracts considerable attention [17; 18; 19; 20]. Moreover, there have been several MEC-related studies associated with its use in vehicular networks [21; 22; 23; 24] and video processing [25; 26]. In Reference [7], we proposed a two-tier computation-offloading framework for multi-user multi-server MEC in 5G HetNets. Different from our previous work that only focused on optimizing the offloading decisions to minimize energy consumption, in this paper, we considered a joint resource allocation and computation-offloading problem, aiming at minimizing the total computing overhead of MDs, including completion time and energy consumption. Using complex optimization techniques and various application constraints, we developed an efficient and low-complexity algorithm capable of high-quality solutions with guaranteed convergence. We found that a high-level heuristic (i.e., meta-heuristic) achieved satisfactory performance in solving a challenging optimization problem using particle swarm optimization (PSO) [27; 28]. Our main contributions include the following:  
* We investigated a two-tier computation-offloading strategy using multi-user multi-server MEC in 5G HetNets.