Future telecommunication systems in beyond 5G/6G networks, will include a massive amount of devices and a high variation of applications, many of which with steep processing requirements and strict latency limitations. To satisfy such demands, Multi-access Edge Computing will play a key role in the future of cloud systems. Users can offload their applications to edge cloud servers, capable of processing their tasks and responding with an output quickly. However, for this to become a reality, it is important to carefully choose a server for each user. This decision is complicated by user mobility and how users could alternatively connect to the remote cloud or execute applications locally. In this article, we propose a heuristic algorithm for determining the best server for each user in a multiple mobile users, multiple servers, multi-tiered scenario. Our proposal considers the time needed for transmitting and processing tasks when minimizing the total service delay as well as the time needed for service setup and migration of data between servers. Moreover, our method attempts to mimic as faithfully as possible real-life scenarios. Finally, analysis shows that our proposal is vastly superior to benchmark methods and even improves upon a solution commonly used in the literature.