The popularity of traditional network services and web content is succeeded by the recent trend in customized services proliferated by the smart devices and gadgets. Fall-risk assessment, augmented reality, ECG (electrocardiography) monitoring, virtual reality-based gaming and similar services are driven through data generated by multi-modal sensors embedded in the end-user equipment. These services may possess varying characteristics and requirements represented with performance metrics and Quality of Service (QoS) parameters. Even though the small form-factor end-user gadgets are getting powerful in terms of resource capacity, they are still incapable of executing complex routines, and thus these tasks should be offloaded to a remote machine. Service-Centric Networks (SCN) focus on delivering customized services to the users in a location-independent fashion. This is in parallel with previous vision put forward by the Information-Centric Networks (ICN) and Content Delivery Networks (CDN), which aim to enhance the end-user experience. The novel set of services for complementing the daily activities of the end-users mostly depicts a latency-intolerant attribute which ultimately calls for a full-fledged resource allocation scheme. Within this context, both computation and networking resources should be allocated optimally, and task assignments should be handled precisely for following the requirements specified by the Service Level Agreements (SLAs). This paper initially presents and discusses problem definitions that should be addressed by the service-centric multi-tier computing architecture that is composed of edge, metro, and cloud servers. In order to achieve this objective, an SLA-aware optimal resource allocation and task assignment model for service-oriented networks is proposed. This optimization model is based on a nonlinear delay formulation for accommodating service-centric network scenarios under various conditions. It is then reshaped as a mixed-integer linear model through piecewise linear approximation. Additionally, a heuristic implementation is presented to address the time and space complexities of the problem for which the aforementioned optimization models remain ineffective. Performance evaluation results show that the proposed solutions are able to find a good allocation of resources while taking the requirements of the services into account. (C) 2019 Elsevier B.V. All rights reserved.