The 5G mobile network will rely on network slicing to provide a wide variety of services with various quality of service (QoS) requirements. Network slicing is promoted by 3GPP and provides a logical vertical partition of the network that is based on network virtualization technologies, namely, network function virtualization (NFV), software-defined networking (SDN) and ETSI multi-access edge computing (MEC). Despite the undisputed benefits in terms of flexibility and scalability that are pledged by the paradigm, network slicing requires intelligent resource scheduling and allocation algorithms to efficiently use the network resources, especially at the edge of the network, due to their scarcity. In this paper, we propose an optimization algorithm for steering data traffic of multiple slices in the edge backhaul network, which aims at maximizing the QoS. We extensively analyze the realizable grade of QoS by testing various levels of MEC resources, demonstrate the beneficial impact of the approach for mobile operators, and highlight the performance advantage that is realized versus a single-slice approach of undifferentiated traffic.INDEX TERMS Multi-access edge computing, network slices, mathematical optimization.