Joint Optimization of Computational Cost and Devices Energy for Task Offloading in Multi-Tier Edge-Clouds

Multi-access edge computing (MEC) has formed a major improvement in the existing mobile cloud computing paradigm, due to its ability in addressing the rising number of latency-sensitive services. However, bearing in mind the limited capacity that edge servers possess which offsets their benefits in the periods of high load, a hierarchical arrangement of the edge cloudlets has been studied and has shown to be successful in expanding their capabilities. Yet, considering the emerging business models in 5G networks, the cost disparity between the edge tiers has been until now ignored, leading to cost-inefficient solutions with respect to the network operators (NOs). In this paper, we consider an NO that is leasing resources of a high-tier central cloudlet for task offload, where we jointly minimize the NO's computational cost and devices' energy consumption in a multi-tier MEC system, by optimizing the offloading decision, the allocated transmission power and radio resources on the uplink channel, and the assigned servers' computation, while respecting the devices' latency requirement. We mathematically formulate our mixed-integer non-convex program and propose a Branch-and-Bound (BnB) algorithm for obtaining the optimal solution. Due to the BnB complexity, we propose a low-complexity algorithm based on the successive convex approximation method to solve and obtain a high-quality solution and also present an inflation-based algorithm for obtaining a polynomial-time and efficient solution. The numerical results show the performance and scalability of the algorithms, demonstrate their efficiency, and uncover insights for helping NOs to better manage their resources following various configurations.