In this paper, a simple and elegant geometric waterfilling (GWF) approach is proposed to solve the unweighted and weighted radio resource allocation problems. Unlike the conventional water-filling (CWF) algorithm, we eliminate the step to find the water level through solving a non-linear system from the Karush-Kuhn-Tucker conditions of the target problem. The proposed GWF requires less computation than the CWF algorithm, under the same memory requirement and sorted parameters. Furthermore, the proposed GWF avoids complicated derivation, such as derivative or gradient operations in conventional optimization methods, while provides insights to the problems and the exact solutions to the target problems. Most importantly, the GWF can be extended to solve a generalized form of radio resource allocation problem with more stringent constraints: (weighted) optimization problem with individual peak power constraints (GWFPP), and to include (weighted) group bounded power constraints (GWFGBP). On the other side, the CWF cannot solve these two general forms of the RRA problems, due to the difficulty to solve the non-linear system with multiple non-linear equations and inequalities in multiple dual variables. Optimality of the proposed water-filling solution is strictly proved for each of the proposed algorithms. Furthermore, numerical results show that the proposed approach is effective, efficient, easy to follow and insight-seeing.Index Terms-Water-filling, channel capacity, optimal radio resource allocation, multi-user MIMO (MU-MIMO), cognitive radio, optimization methods.

Abstract-Merging mobile edge computing (MEC) functionality with the dense deployment of base stations (BSs) provides enormous benefits such as a real proximity, low latency access to computing resources. However, the envisioned integration creates many new challenges, among which mobility management (MM) is a critical one. Simply applying existing radio access oriented MM schemes leads to poor performance mainly due to the co-provisioning of radio access and computing services of the MEC-enabled BSs. In this paper, we develop a novel user-centric energy-aware mobility management (EMM) scheme, in order to optimize the delay due to both radio access and computation, under the long-term energy consumption constraint of the user. Based on Lyapunov optimization and multi-armed bandit theories, EMM works in an online fashion without future system state information, and effectively handles the imperfect system state information. Theoretical analysis explicitly takes radio handover and computation migration cost into consideration and proves a bounded deviation on both the delay performance and energy consumption compared to the oracle solution with exact and complete future system information. The proposed algorithm also effectively handles the scenario in which candidate BSs randomly switch on/off during the offloading process of a task. Simulations show that the proposed algorithms can achieve close-to-optimal delay performance while satisfying the user energy consumption constraint.

The (ultra-)dense deployment of small-cell base stations (SBSs) endowed with cloud-like computing functionalities paves the way for pervasive mobile edge computing (MEC), enabling ultra-low latency and location-awareness for a variety of emerging mobile applications and the Internet of Things. To handle spatially uneven computation workloads in the network, cooperation among SBSs via workload peer offloading is essential to avoid large computation latency at overloaded SBSs and provide high quality of service to end users. However, performing effective peer offloading faces many unique challenges due to limited energy resources committed by self-interested SBS owners, uncertainties in the system dynamics and co-provisioning of radio access and computing services. This paper develops a novel online SBS peer offloading framework, called OPEN, by leveraging the Lyapunov technique, in order to maximize the long-term system performance while keeping the energy consumption of SBSs below individual long-term constraints. OPEN works online without requiring information about future system dynamics, yet provides provably near-optimal performance compared to the oracle solution that has the complete future information. In addition, this paper formulates a peer offloading game among SBSs, analyzes its equilibrium and efficiency loss in terms of the price of anarchy to thoroughly understand SBSs' strategic behaviors, thereby enabling decentralized and autonomous peer offloading decision making. Extensive simulations are carried out and show that peer offloading among SBSs dramatically improves the edge computing performance.

The vehicular edge computing (VEC) system integrates the computing resources of vehicles, and provides computing services for other vehicles and pedestrians with task offloading. However, the vehicular task offloading environment is dynamic and uncertain, with fast varying network topologies, wireless channel states and computing workloads. These uncertainties bring extra challenges to task offloading. In this work, we consider the task offloading among vehicles, and propose a solution that enables vehicles to learn the offloading delay performance of their neighboring vehicles while offloading computation tasks. We design an adaptive learning-based task offloading (ALTO) algorithm based on the multi-armed bandit (MAB) theory, in order to minimize the average offloading delay. ALTO works in a distributed manner without requiring frequent state exchange, and is augmented with input-awareness and occurrence-awareness to adapt to the dynamic environment. The proposed algorithm is proved to have a sublinear learning regret. Extensive simulations are carried out under both synthetic scenario and realistic highway scenario, and results illustrate that the proposed algorithm achieves low delay performance, and decreases the average delay up to 30% compared with the existing upper confidence bound based learning algorithm.Index Terms-Vehicular edge computing, task offloading, online learning, multi-armed bandit.

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