# Mobility- and Energy-Aware Cooperative Edge Offloading for Dependent Computation Tasks +
## 5 Solution of Dynamic Computation Offloading Optimization Problem
### Energy-Efficient Task Offloading (EETO) Algorithm
ASO and CMO execute all tasks on MEC servers within 2 s; thus, even if the deadline \(T_{d}^{\max}\) increases, the energy consumption remains essentially constant. However, an increasing deadline \(T_{d}^{\max}\) allows energy-efficient helpers to execute tasks, even if they have long processing times, thus reducing the CPCO and EETO energy consumption. By optimally trading off the task execution options, EETO achieves some moderate energy reductions for the heterogeneous task scenarios in Figure 8 compared to the minimum of the CMO and CPCO energy consumptions. Importantly, EETO flexibly achieves the minimum energy consumption across the entire examined \(T_{d}^{\max}\) range. ## 7 Conclusions

### Summary of This Article

We developed and evaluated the novel Energy-Efficient Task Offloading (EETO) algorithm for dependent computation tasks in a cooperative edge computing setting with mobile end devices that contribute computation and communication relay support in a sliced edge network environment. EETO accommodates arbitrary task dependencies that are characterized by a general task dependency graph and employs a deep-learning-based trajectory prediction for the device sojourn times in the wireless transmission ranges. We have formulated the task offloading optimization problem as a quadratically constrained quadratic programming (QCQP) problem and developed a solution strategy that obtains the task offloading decisions through a semidefinite relaxation and stochastic mapping from the QCQP solution. The simulation evaluations indicate the EETO consistently achieves low battery energy consumption across heterogeneous parameter settings and scenarios. In particular, the EETO substantially outperforms naive benchmarks that compute the tasks locally or offload all tasks to MEC servers. EETO also outperforms benchmarks with a limited set of offloading decision options; specifically, we considered benchmarks that allow helper nodes to only function as task processing (computations) nodes (CPCO) or to only function as task communication (relay) nodes for offloading to an MEC server (CMCO). We found that the CPCO and CMOO benchmarks attain the EETO performance in some scenarios, while in other scenarios, the EETO achieves significant performance gains. Figure 8: Average battery energy consumption vs. task execution deadline \(T_{d}^{\max}\); fixed parameters: uniform random data size \(b_{k}=150\)–\(180\) KB, random task dependency. (**a**) Overall deadline \(FT_{K}<T_{d}^{\max}\), \(c_{k}=15\)–\(55\) cycles/bit, (**b**) deadlines for ind. tasks \(FT_{k}\), \(c_{k}=32\)–\(38\) cycles/bit. ### Limitations and Future Research Directions

A limitation of the developed EETO algorithm is the computational effort for solving the QCQP, as noted in Section 5. One strategy for simplifying the QCQP could be to reduce the considered task offloading options for scenarios where a limited set of options achieve or nearly achieve the optimal EETO performance. For instance, a machine learning approach could learn the scenarios where a limited set of offloading options, such as the naive options or CPCO or CMCO, closely approach the EETO performance and then consider only the reduced set of offloading options in the solution of the optimization problem. Based on training data sets that can be created with the optimal EETO offloading decision making developed in this article, future research could investigate such simplified offloading strategies for scenarios that would need to be identified with pre-trained machine learning models. Another strategy for simplifying the QCQP could be to \"thin\" out the set of potential helper nodes or MEC server nodes that are considered for task offloading, that is, the helper and MEC server nodes to be considered in the solution of the QCQP could be pre-selected according to criteria that indicate a high level of potential usefulness of a helper or MEC server.