The distributed edge computing network has been proposed as a promising approach to accelerate task computation. Incorporating parallel edge computing, we investigate a parallel distributed edge computing network where each edge device is allowed to receive one task and compute another task simultaneously, and meanwhile, edge devices are allowed to compute their respectively received tasks simultaneously. We minimize the total task completion time (TCT) of source nodes by jointly optimizing offloading selections of source nodes and scheduling order of task offloading, i.e., MTOS problem, which is proved to be NP-hard. To tackle it, we first study the MTOS problem with one edge device (MTOS-1), establish three task offloading rules to minimize the total TCT, and propose a priority-based scheduling order of task offloading algorithm. Based on the established task offloading rules for the MTOS-1 problem, we study the MTOS problem withMedge devices and additional offloading-adjacency constraint (MTOSO-M), establish another two task offloading rules for scheduling order, and propose an automatic adjustment-based joint offloading selections and scheduling order algorithm. By relaxing the offloading-adjacency constraint of the MTOSO-Mproblem, we further study the general MTOS problem withMedge devices (MTOS-M), derive a lower bound of the total TCT, and propose a queue jumping-based joint offloading selections and scheduling order algorithm. Extensive numerical results are conducted to discuss impacts of vital network parameters on the total TCT, verify the superiority of the proposed algorithms, and show that the communication-computation parallelism for edge devices and the computation parallelism among edge devices further reduce the total TCT.

To enable resource-constrained wireless devices (WDs) to process the computation-intensive and latency-sensitive computation tasks, the wireless powered mobile edge computing (WP-MEC) network has been proposed as a promising approach. Incorporating mobile cloud computing (CC) in the WP-MEC network, we investigate the wireless powered mobile edge-CC (WP-MECC) network, where the WDs first harvest energy from a hybrid access point (HAP), and then consume the harvested energy to compute the tasks locally, offload them to the HAP for computation, or offload them to the cloud server (CS) via the relaying of the HAP. To pursue fairness among the WDs, we minimize the maximum task completion time (TCT) of WDs by jointly optimizing the time resources, computing mode selection, and computation resources. We prove the minimization problem is NP-hard. To tackle the problem, we decompose it into the subproblem and top problem, and propose an alternate optimization-based resource allocation and the computing mode selection (ARACM) algorithm with low computational complexity, which achieves a comparable performance with the exhaustive search method in terms of the minimal maximum TCT of WDs. Moreover, we propose a deep reinforcement learning (DRL)-based resource allocation and the computing mode selection (DRACM) algorithm with less execution latency than the ARACM algorithm. Numerical results show that the two proposed algorithms achieve satisfactory performance in terms of the minimal maximum TCT of WDs and execution latency.