Mobile devices are naturally limited due to their portable sizes and will therefore never be equal to their desktop counterparts. To overcome this, Edge Cloud Computing can be utilized to execute tasks on behalf of the devices, allowing them to run applications that would normally be too demanding. In this service model, it is important to maintain a low Service Delay to keep the service transparent to the user. This can be achieved by focusing on lowering the Transmission Delay and Processing Delay. While existing approaches in the literature focus on one of those two, we postulate that only when considering both delays you can efficiently lower Service Delay and provide quality to all applications. In order to do that while being feasible, we propose a method based on Particle Swarm Optimization for lowering Service Delay in Edge Cloud Computing. Our proposal is shown to be close to optimality while still maintaining a low execution time for multiple cloudlets scenarios. Moreover, our proposal outperforms existing approaches from the literature with single focus on computation or communication, even in situations with high processing and transmission burdens, proving the superiority of a dual focus approach.