## Yanfei He* and Zhenhua Tang*## |

MEC system parameters | Value |
---|---|

Subcarrier width | [TeX:] $$B_{N}=15 \mathrm{kHz}$$ |

Background noise | [TeX:] $$\delta^{2}=-75 \mathrm{dBm}$$ |

Maximum transmission power | [TeX:] $$P^{m}=600 \mathrm{~mW}$$ |

Input data size | [TeX:] $$D_{i}=1000 \mathrm{bits}$$ |

Task computational complexity | [TeX:] $$X_{i} \in[1000,1200] \text { cycles/bits }$$ |

Task execution delay constraints | [TeX:] $$\tau_{i} \in[9,10] \mathrm{ms}$$ |

User CPU frequency | [TeX:] $$f_{i, l o c} \in[0.6,0.7] \mathrm{GHz}$$ |

MEC server frequency | [TeX:] $$f_{k, s e r} \in[1.1,1.2] \mathrm{GHz}$$ |

Fig. 3 evaluates the task execution cost, and compares our proposed algorithm with the algorithms in [19] and [20] under different conditions of noise power (background noises are -75, -80, -85, and -90 dBm, respectively); the relationship between task execution overheads and different amounts of task input data is illustrated.

Fig. 3 shows that the task execution cost of our proposed strategy and the algorithms proposed in [19] and [20] all increase with the amount of task input data. As the increase in the amount of input data increases task execution delay and increases task execution energy consumption, this in turn will increase the task execution overheads. Furthermore, the task execution cost of the proposed algorithm is better than the task execution cost of algorithms proposed in [19] and [20]. The reason is that the algorithms proposed in [19] and [20] aim to optimize the task execution delay, which may lead to higher task execution energy consumption and increase the task execution overheads. The algorithm proposed in this paper models the distributed computation offloading decision between the mobile equipment as a multiuser computation offloading game, achieving a balance between the user diversity and the MEC server diversity.

Fig. 4 demonstrates the relationship between task execution overheads and the computing power of MEC servers, and shows the comparison among the algorithms proposed in [19] and [20]. It can be seen from this figure that the task execution cost of our proposed algorithm as well as of [19] and [20] all decrease with the increase of the computing power for MEC servers. The reason is that increasing the computing power of MEC servers can improve the task execution performance and reduce task execution overheads. By comparing the curves obtained by the three algorithms, it is evident that our proposed algorithm is superior to the algorithms proposed in [19] and [20].

Fig. 5 compares the relationship between the algorithm task execution cost and the number of requested users of our proposed algorithm and the two proposed in [19] and [20]. As can be seen from this figure, as the number of requested users increases, the task execution overheads increase. Compared with other algorithms, the proposed algorithm has the lowest task execution cost. The reason is that the proposed algorithm offloads mobile node's own computing tasks to edge servers. It comprehensively considers several factors, for example, energy consumption, delay, cost, resource usage, contribution or profit of different types of tasks, and reduces the overall overheads of computation offloading. This allows multiusers to efficiently perform the computational offloading under the game model. The performance gap of each algorithm increases as the number of requested users increases. The reason is that when the number of requested users increases, the resource competition at MEC servers will cause the system performance to decrease.

The algorithm designed in this paper first calculates the unloading weight, and then the distributed time slot is iterated to update the unloading decision. In summary, our proposed algorithm can effectively increase the number of useful decision-making users, and can achieve the balance by a limited number of iterations. Under the Nash equilibrium, the final decision strategy shows self-stability. The user has no incentive to unilaterally change decisions, serving as a relatively stable final offloading decision plan for this period of time. At the same time, the proposed algorithm is superior to several other offloading algorithms in terms of the number of users and overall overheads for beneficial decision-making.

This paper discusses offloading strategies in a multi-user and multi-server scenario. In a resourceconstrained system, we propose a multi-user and multi-server MEC task offloading algorithm based on cost optimization. The algorithm is verified by simulation experiments, and simulation results show that our proposed algorithm has a good offloading performance. In terms of the number of users and overall overheads for beneficial decision-making, the algorithm is superior to several other computation offloading algorithms. Notwithstanding, there are still a few problems that need further discussion and optimization. This paper assesses the task offloading weight by calculating the reward of tasks. The weight is mainly used to investigate the decision of mobile equipment to calculate locally or offload to edge servers. There is hardly any study of the impact of offloading weight in the case of performing service migration when the edge server has insufficient computing power. Therefore, it is suggested that future work can address the issue of service migration, and discuss the impact of offloading weight during service migration.

- 1 Y. S. Jeong, J. H. Park, "Security, privacy, and efficiency of sustainable computing for future smart cities,"
*Journal of Information Processing Systems*, vol. 16, no. 1, pp. 1-5, 2020.custom:[[[-]]] - 2 W. Liu, L. Zhang, Z. Zhang, C. Gu, C. Wang, M. O'neill, F. Lombardi, "XOR-based low-cost recon-figurable PUFs for IoT security,"
*ACM Transactions on Embedded Computing Systems (TECS)*, vol. 18, no. 3, pp. 1-21, 2019.custom:[[[-]]] - 3 V. Kumar, G. Sakya, C. Shankar, "WSN and IoT based smart city model using the MQTT protocol,"
*Journal of Discrete Mathematical Sciences and Cryptography*, vol. 22, no. 8, pp. 1423-1434, 2019.custom:[[[-]]] - 4 W. Shi, X. Zhang, Y. Wang, Q. Zhang, "Edge computing: state-of-the-art and future directions,"
*Journal of Computer Research and Development*, vol. 56, no. 1, pp. 69-89, 2019.custom:[[[-]]] - 5 E. Kim, S. Kim, "An efficient software defined data transmission scheme based on mobile edge computing for the massive IoT environment,"
*KSII Transactions on Internet Information Systems*, vol. 12, no. 2, pp. 974-987, 2018.doi:[[[10.3837/tiis.2018.02.027]]] - 6 T. Quack, M. Bosinger, F. J. Heßeler, D. Abel, "Infrastructure-based digital maps for connected autonomous vehicles,"
*at-Automatisierungstechnik*, vol. 66, no. 2, pp. 183-191, 2018.doi:[[[10.1515/auto-2017-0100]]] - 7 M. C. Filippou, D. Sabella, V. Riccobene, "Flexible MEC service consumption through edge host zoning in 5G networks," in
*Proceedings of 2019 IEEE Wireless Communications and Networking Conference Workshop (WCNCW)*, Marrakech, Morocco, 2019;pp. 1-6. custom:[[[-]]] - 8 K. Kanai, K. Imagane, J. Katto, "Overview of multimedia mobile edge computing,"
*ITE Transactions on Media Technology and Applications*, vol. 6, no. 1, pp. 46-52, 2018.custom:[[[-]]] - 9 M. Li, F. R. Y u, P. Si, Y. Zhang, "Green machine-to-machine communications with mobile edge computing and wireless network virtualization,"
*IEEE Communications Magazine*, vol. 56, no. 5, pp. 148-154, 2018.doi:[[[10.1109/MCOM.2018.1601005]]] - 10 Q. Fan, N. Ansari, "Application aware workload allocation for edge computing-based IoT,"
*IEEE Internet of Things Journal*, vol. 5, no. 3, pp. 2146-2153, 2018.doi:[[[10.1109/JIOT.2018.2826006]]] - 11 Y. Mao, J. Zhang, K. B. Letaief, "Joint task offloading scheduling and transmit power allocation for mobile-edge computing systems," in
*Proceedings of 2017 IEEE Wireless Communications and Networking Conference (WCNC)*, San Francisco, CA, 2017;pp. 1-6. custom:[[[-]]] - 12 C. Wang, F. R. Y u, C. Liang, Q. Chen, L. Tang, "Joint computation offloading and interference management in wireless cellular networks with mobile edge computing,"
*IEEE Transactions on V ehicular Technology*, vol. 66, no. 8, pp. 7432-7445, 2017.doi:[[[10.1109/TVT.2017.2672701]]] - 13 A. De La Oliva, X. C. Perez, A. Azcorra, A. Di Giglio, F. Cavaliere, D. Tiegelbekkers, et al., "Xhaul: toward an integrated fronthaul/backhaul architecture in 5G networks,"
*IEEE Wireless Communications*, vol. 22, no. 5, pp. 32-40, 2015.doi:[[[10.1109/MWC.2015.7306535]]] - 14 J. Liu, Q. Zhang, "Offloading schemes in mobile edge computing for ultra-reliable low latency communications,"
*IEEE Access*, vol. 6, pp. 12825-12837, 2018.doi:[[[10.1109/ACCESS.2018.2800032]]] - 15 Q. D. Thinh, J. Tang, D. La Quang, T. Q. Quek, "Adaptive computation scaling and task offloading in mobile edge computing," in
*Proceedings of 2017 IEEE Wireless Communications and Networking Conference (WCNC)*, San Francisco, CA, 2017;pp. 1-6. custom:[[[-]]] - 16 G. Zhang, X. Liu, "Tasks split and offloading scheduling decision in mobile edge computing with limited resources,"
*Computer Applications and Software*, vol. 36, no. 10, pp. 268-278, 2019.custom:[[[-]]] - 17 S. S. Tanzil, O. N. Gharehshiran, V. Krishnamurthy, "Femto-cloud formation: a coalitional game-theoretic approach," in
*Proceedings of 2015 IEEE Global Communications Conference (GLOBECOM)*, San Diego, CA, 2015;pp. 1-6. custom:[[[-]]] - 18 T. Q. Dinh, J. Tang, Q. D. La, T. Q. Quek, "Offloading in mobile edge computing: task allocation and computational frequency scaling,"
*IEEE Transactions on Communications*, vol. 65, no. 8, pp. 3571-3584, 2017.doi:[[[10.1109/TCOMM.2017.2699660]]] - 19 Y. Mao, J. Zhang, S. H. Song, K. B. Letaief, "Stochastic joint radio and computational resource management for multi-user mobile-edge computing systems,"
*IEEE Transactions on Wireless Communi-cations*, vol. 16, no. 9, pp. 5994-6009, 2017.doi:[[[10.1109/TWC.2017.2717986]]] - 20 L. Huang, X. Feng, C. Zhang, L. Qian, Y. Wu, "Deep reinforcement learning-based joint task offloading and bandwidth allocation for multi-user mobile edge computing,"
*Digital Communications and Networks*, vol. 5, no. 1, pp. 10-17, 2019.custom:[[[-]]] - 21 Y. Wei, Z. Zhang, F. R. Y u, Z. Han, "Joint user scheduling and content caching strategy for mobile edge networks using deep reinforcement learning," in
*Proceedings of 2018 IEEE International Conference on Communications Workshops (ICC Workshops)*, Kansas City, MO, 2018;pp. 1-6. custom:[[[-]]] - 22 B. Bi, Y. J. Zhang, "Computation rate maximization for wireless powered mobile-edge computing with binary computation offloading,"
*IEEE Transactions on Wireless Communications*, vol. 17, no. 6, pp. 4177-4190, 2018.doi:[[[10.1109/TWC.2018.2821664]]] - 23 I. Dragan, "Egalitarian allocations and the inverse problem for the Shapley value,"
*American Journal of Operations Research*, vol. 8, no. 6, 2018.custom:[[[-]]] - 24 W. Y ang, J. Liu, X. Liu, "Existence of fuzzy Zhou bargaining sets in TU fuzzy games,"
*International Journal of Fuzzy System Applications (IJFSA)*, vol. 7, no. 1, pp. 46-55, 2018.doi:[[[10.4018/IJFSA.2018010104]]] - 25 S. Sasikala, S. A. alias Balamurugan, S. Geetha, "n efficient feature selection paradigm using PCA-CFS-Shapley values ensemble applied to small medical data sets," in
*Proceedings of 2013 4th International Conference on Computing*, Communications and Networking Technologies (ICCCNT), Tiruchengode, India, 2013;pp. 1-5. custom:[[[-]]] - 26 M. Gusev, S. Dustdar, "Going back to the roots: the evolution of edge computing, an iot per-spective,"
*IEEE Internet Computing*, vol. 22, no. 2, pp. 5-15, 2018.custom:[[[-]]] - 27 J. Xu, Z. K. Yang, W. Y uan, "Heterogeneous channel assignment of multi-radio multi-channel wireless networks: a game theoretic approach,"
*Journal of Chinese Computer Systems*, vol. 33, no. 5, pp. 1053-1056, 2012.custom:[[[-]]] - 28 Z. Huo, X. Li, S. Jin, Z. Wang, "Nash equilibrium of an energy saving strategy with dual rate transmission in wireless regional area network,"
*Wireless Communications and Mobile Computing*, vol. 2017, no. 9053862, 2017.doi:[[[10.1155//9053862]]] - 29 Y. Yang, Y. Li, W. Zhang, F. Qin, P. Zhu, C. X. Wang, "Generative-adversarial-network-based wireless channel modeling: challenges and opportunities,"
*IEEE Communications Magazine*, vol. 57, no. 3, pp. 22-27, 2019.custom:[[[-]]] - 30 K. De V ogeleer, G. Memmi, P. Jouvelot, F. Coelho, "The energy/frequency convexity rule: modeling and experimental validation on mobile devices,"
*in Parallel Processing and Applied Mathematics. HeidelbergGermany: Springer*, pp. 793-803, 2013.custom:[[[-]]] - 31 F. Wang, J. Xu, X. Wang, S. Cui, "Joint offloading and computing optimization in wireless powered mobile-edge computing systems,"
*IEEE Transactions on Wireless Communications*, vol. 17, no. 3, pp. 1784-1797, 2018.doi:[[[10.1109/TWC.2017.2785305]]]