There are many applications which cannot be executed by mobile devices due to their limitations in memory, processing, battery, among others. One solution to this would be offloading heavy tasks to cloud servers in the edge of the network, in a service model called Edge Cloud Computing. The main Quality of Service requirement of this model is a low Service Delay, which can be achieved by lowering Transmission Delay and Processing Delay. Works in literature focus on either one of those two types of delay. This paper, however, argues that an approach which combines transmission and processing technologies to lower Service Delay would be more efficient. This idea is defended by an analysis of the service model and existing stochastic modeling of the Edge Cloud Computing system. We conclude that a dual focus approach would be the only way of truly minimizing the Service Delay, therefore being the desired method to improve Quality of Service. We conclude by laying the foundation for a future model that follows such concept.