By executing offloaded tasks from mobile users, edge computing augments mobile devices with computing/communications resources from edge nodes (ENs), thus enabling new services/applications (e.g., real-time gaming, virtual/augmented reality). However, despite being more resourceful than mobile devices, allocating ENs' computing/communications resources to a given favorable set of users (e.g., closer to edge nodes) may block other devices from their services. This is often the case for most existing task offloading and resource allocation approaches that only aim to maximize the network social welfare or minimize the total energy consumption but do not consider the computing/battery status of each mobile device. This work develops an energy-based proportionally fair task offloading and resource allocation framework for a multi-layer cooperative edge computing network to serve all user equipments (UEs) while considering both their service requirements and individual energy/battery levels. The resulting optimization involves both binary (offloading decisions) and continuous (resource allocation) variables. To tackle the NP-hard mixed integer optimization problem, we leverage the fact that the relaxed problem is convex and propose a distributed algorithm, namely the dynamic branch-and-bound Benders decomposition (DBBD). DBBD decomposes the original problem into a master problem (MP) for the offloading decisions and multiple subproblems (SPs) for resource allocation. To quickly eliminate inefficient offloading solutions, the MP is integrated with powerful Benders cuts exploiting the ENs' resource constraints. We then develop a dynamic branch-and-bound algorithm (DBB) to efficiently solve the MP considering the load balance among ENs. The SPs can either be solved for their closed-form solutions or be solved in parallel at ENs, thus reducing the complexity. The numerical results show that the DBBD returns the optimal solution in maximizing the proportional fairness among UEs. The DBBD has higher fairness indexes, i.e., Jain's index and min-max ratio, in comparison with the existing ones that minimize the total consumed energy.

By executing offloaded tasks from mobile users, edge computing augments mobile devices with computing/communications resources from edge nodes (ENs), enabling new services/applications (e.g., real-time gaming, virtual/augmented reality). However, despite being more resourceful than mobile devices, allocating ENs’ computing/communications resources to given favorable sets of users may block other devices from their service. This is often the case for most existing task offloading and resource allocation approaches that only aim to maximize the network social welfare (e.g., minimizing the total energy consumption) but not consider the computing/battery status of each mobile device. This work develops a proportional fair task offloading and resource allocation framework for a multi-layer cooperative edge computing network to serve all user equipment (UEs) while considering both their service requirements and individual energy/battery levels. The resulting optimization involves both binary (offloading decisions) and real variables (resource allocations), making it NP-hard. To tackle it, we leverage the fact that the relaxed problem is convex and propose a distributed algorithm, namely the dynamic branchand-bound Benders decomposition (DBBD). DBBD decomposes the original problem into a master problem (MP) for the offloading decision and subproblems (SPs) for resource allocation. The SPs can either find their closed-form solutions or be solved in parallel at ENs, thus help reduce the complexity. The numerical results show that the DBBD returns the optimal solution of the problem maximizing the fairness between UEs. The DBBD has higher fairness indexes, i.e., Jain’s index and min-max ratio, in comparing with the existing ones that minimize the total consumed energy.

We develop a joint offloading and resource allocation framework for a multi-layer cooperative fog computing network, aiming to minimize the total energy consumption of multiple mobile devices subject to their service delay requirements. The resulting optimization involves both binary (offloading decisions) and real variables (resource allocations), making it an NP-hard and computationally intractable problem. To tackle it, we first propose an improved branch-and-bound algorithm (IBBA) that is implemented in a centralized manner. However, due to the large size of the cooperative fog computing network, the computational complexity of the proposed IBBA is relatively high. To speed up the optimal solution searching as well as to enable its distributed implementation, we then leverage the unique structure of the underlying problem and the parallel processing at fog nodes. To that end, we propose a distributed framework, namely feasibility finding Benders decomposition (FFBD), that decomposes the original problem into a master problem for the offloading decision and subproblems for resource allocation. The master problem (MP) is then equipped with powerful cutting-planes to exploit the fact of resource limitation at fog nodes. The subproblems (SP) for resource allocation can find their closed-form solutions using our fast solution detection method. These (simpler) subproblems can then be solved in parallel at fog nodes. The numerical results show that the FFBD always returns the optimal solution of the problem with significantly less computation time (e.g., compared with the centralized IBBA approach). The FFBD with the fast solution detection method, namely FFBD-F, can reduce up to 60% and 90% of computation time, respectively, compared with those of the conventional FFBD, namely FFBD-S, and IBBA.

We investigate a joint offloading and resource allocation under a multi-layer cooperative fog and cloud computing architecture, aiming to minimize the total energy consumption of mobile devices while meeting users' QoS requirements, e.g., delay, security, and application compatibility. Due to the mutual coupling amongst offloading decision and resource allocation variables, the resulting optimization is a mixed integer non- linear programming problem that is NP-hard. Such problem often requires exponential time to find the optimal solution. In this work, we propose a distributed approach, namely feasibility-finding Benders decomposition (FFBD), that decomposes the original problem into a master problem for the offloading decision and subproblems for resource allocation. These (simpler) subproblems can be solved in parallel at fog nodes, thereby reducing both the complexity and the computational time. The numerical results show that the FFBD always returns the optimal solution of the problem with significantly less computation time (e.g., in comparing with the branch-and-bound method).

We propose a novel edge computing network architecture that enables edge nodes to cooperate in sharing computing and radio resources to minimize the total energy consumption of mobile users while meeting their delay requirements. To find the optimal task offloading decisions for mobile users, we first formulate the joint task offloading and resource allocation optimization problem as a mixed integer non-linear programming (MINLP). The optimization involves both binary (offloading decisions) and real variables (resource allocations), making it an NP-hard and computational intractable problem. To circumvent, we relax the binary decision variables to transform the MINLP to a relaxed optimization problem with real variables. After proving that the relaxed problem is a convex one, we propose two solutions namely ROP and IBBA. ROP is adopted from the interior point method and IBBA is developed from the branch and bound algorithm. Through the numerical results, we show that our proposed approaches allow minimizing the total energy consumption and meet all delay requirements for mobile users.

We propose a two dimension (2D) proactive uplink resource allocation (2D-PURA) algorithm that aims to reduce the delay/latency in event-based machine-type communications (MTC) applications. Specifically, when an event of interest occurs at a device, it tends to spread to the neighboring devices. Consequently, when a device has data to send to the base station (BS), its neighbors later are highly likely to transmit. Thus, we propose to cluster devices in the neighborhood around the event, also referred to as the disturbance region, into rings based on the distance from the original event. To reduce the uplink latency, we then proactively allocate resources for these rings. To evaluate the proposed algorithm, we analytically derive the mean uplink delay, the proportion of resource conservation due to successful allocations, and the proportion of uplink resource wastage due to unsuccessful allocations for 2D-PURA algorithm. Numerical results demonstrate that the proposed method can save over 16.5 and 27 percent of mean uplink delay, compared with the 1D algorithm and the standard method, respectively.