## Taoyu Deng , Yueyun Chen , Guang Chen , Meijie Yang and Liping Du## |

Parameters | Values |
---|---|

weighting factor | 0–1 |

computation workload | 40 cycles/bit |

proportion between task result and itself | 0.2 |

transmit speed on the high-speed optical fiber | [TeX:] $$10^{10}$$ bit/s |

C task data size | 1–10 Mbits |

Transmission frequency | 5.9GHz |

f computation ability of MECs | 8 × [TeX:] $$10^{9}$$ cycles/s |

h channel gain | Rayleigh fading channel |

[TeX:] $$N_0$$ power spectral density | 3 × 10−13 W |

[TeX:] $$T_{\max }$$ vehicle’s task latency upper bound | 30 ms |

[TeX:] $$P_{\max }$$ vehicle’s transmit power upper bound | 0.2 W |

Fig. 2 represents the latency performance in terms of the task data size. It shows the task data size that can be executed by different methods while meeting the 20 ms delay requirement of IoV application. We can also see that latency increases with the increase of task data size and the curve is linear. This is because task data size C is in direct proportion to [TeX:] $$T_{\text {total }}$$. As we deduced in part II, [TeX:] $$T_{\text {total }}=T_{\text {edge }}+T_s$$, and we can obtain from equation (5) and equation (7) that C is in direct proportion to [TeX:] $$T_{\text {edge }} \text { and } T_s \text {. }$$ Hence, C is in direct proportion to [TeX:] $$T_{\text {total }}$$, which makes the curve linear. And proposed MEC cooperation strategy shows less latency than the three baseline strategies. Moreover,with the increase of the number of cooperation MECs, latency performance shows more superiority. This is because the proposed strategy splits the tasks properly and uses the resources more rationally.

The latency performance in terms of the task data size is shown in Fig. 3, in which K is equal to 3. It indicates the proportion of chain latency and edge latency in Fig. 2. We can observe that edge latency occupies more proportion of the total latency, and the proportion between chain latency and edge latency remains unchanged with the increase of task data size. This is because the task preference index and the number of MEC servers remain unchanged, the proportion will change when these two parameters change.

Fig. 4 represents the total cost performance in terms of latency requirement. As shown in Fig. 4, the total cost first decreases and then remains unchanged as the latency requirement [TeX:] $$T_{\max }$$ increases. We can also see that, the proposed strategy can reach more rigorous latency requirements while consuming less total cost. It can be concluded from Fig. 4 that, the proposed MEC cooperation partial offloading strategy can satisfy the requirement of L2SC tasks while saving energy, which is more suitable for L2SC tasks.

The energy consumption performance in terms of latency requirement is illustrated in Fig. 5. We can observe that energy consumption first decreases and then remains unchanged as the latency requirement increases. We can also see that, comparing with the three baseline strategies, the proposed strategy can reach more rigorous latency requirements when the energy consumption is the same, and the proposed strategy shows more superiority when approaching the minimum latency requirement that the strategy can reach(more suitable for low latency scene). Besides, with the increase of the number of cooperation MECs, energy consumption performance shows more superiority.

Fig. 6 represents the latency performance in terms of latency requirement. It can be seen that latency first increases and then remains unchanged as the latency requirement [TeX:] $$T_{\max }$$ increases. We can also see that the proposed strategy shows less latency than the three baseline strategies and can satisfy more rigorous latency requirements, and with the increase of the number of cooperation MECs, latency performance shows more superiority.

The latency performance in terms of task preference is shown in Fig. 7. It shows that latency decreases with the increase of task preference index. This is because a large indicates the user’s low latency tolerance, where we should enhance our latency performance to meet the user’s requirement. Besides, with the increase of the number of cooperation MECs, latency performance shows more superiority.

The energy consumption performance in terms of task preference index is shown in Fig. 8. It indicates that energy consumption increases with the increase of task preference index. This is because a small indicates the user’s low energy consumption tolerance, where we should enhance our energy consumption performance to meet the user’s requirement.

Figs. 9 and 10 show the influence of different task preference indexes for the proposed method(where we set K = 3 as an example). We can observe from Fig. 9 that the proposed method can reach a better latency performance when choosing a higher task preference index. And with the increase of the task data size, latency performance shows more superiority. Fig. 10 shows the energy consumption performance in terms of task data size for different task preference indexes. It shows that the proposed method can reach a better energy consumption performance when choosing a lower task preference index, and with the increase of the task data size, energy consumption performance shows more superiority.

In this paper, we investigate an edge collaborative task serial offloading parallel executing strategy in MEC-enabled IoV networks, which can split the task on the edge and use several MEC servers to paralleling execute each part of the task. And we formulate the problem as the minimization of the weighted sum of the energy consumption and the latency which is non-smooth and non-convex. An alternate convex search algorithm is provided to tackle the problem efficiently, which can converge to a sub-optimal solution. The numerical simulation results show that the proposed multi-MEC cooperating partial offloading strategy can take advantage of the roadside computing resources properly, and shows superiority in the weighted sum of latency and energy consumption. When latency requirement becomes more relaxed, the proposed strategy can further reduce the total cost. And for different tasks, the proposed strategy can also change dynamically to meet their needs by adjusting the task preference index. Moreover, the impacts of various parameters were revealed, which validate the feasibility of the proposed method in different situations. For future investigation, we plan to study the multi-task condition, and schedule the offloading sequence based on priority and task sequence. To solve the multi-task arriving problem, we will also study queuing issues.

It is obvious that the optimal solution of problem (14) is obtain at the minimum point of [TeX:] $$T_n$$, we can derive from C8, C9, and C10 that

to reach the minimum value of this max function, we need each part of the fuction to take the same value:

Based on function (21), we can obtain that

Finally, we can derive from C1, C2, and [TeX:] $$\eta_f+\eta_l+\sum_{i \in I} \eta_i=1$$ that

Proof of the convexity: Let f(a) represent the objective of (18) as

The second-order derivative of f(a) in terms of a can be written as

It is easy to obtain that the second-order derivative is always positive because a > 0 , and it is also obvious that the constraints are convex. Hence, f(a) is a convex function, and problem (18) is a convex optimization problem. The proof is finished.

Proof of the analytical solution: Because the second order derivative of f(a) is always positive, the first order derivative is a monotonously increasing function with a. Moreover, the first order derivative satisfies [TeX:] $$\lim _{a \rightarrow+\infty} f^{\prime}(a)=\delta c>0$$ and [TeX:] $$\lim _{a \rightarrow 0} f^{\prime}(a) \rightarrow-\infty<0.$$ Therefore, [TeX:] $$f^{\prime}(a)$$ has and only has one zero point, which is the unique minum point of f(a). As a result, the minum value of f(a) is obtained at its minum point where [TeX:] $$f^{\prime}(a)=0$$. The proof is finished.

Taoyu. Deng received the B.S. degree from University of Science and Technology Beijing, in 2019. He is currently pursuing his M.S degree with the School of Computer and Communication Engineer- ing, University of Science and Technology Beijing, China. His current research interests are mobile edge computing and Internet of vehicles.

Yueyun. Chen is a Professor of Information and Communication Engineering at University of Sci- ence and Technology Beijing. She graduated with a B.S. degree in Radio Technology from South China University of Technology, and M.S. and Ph.D. degrees in Communication and Information System from Beijing Jiaotong University, respectively. Her research interesting includes wireless mobile com- munication, AI in wireless communications, radio signal processing, massive MIMO, wireless net- works, space information and communication sys- tems, massive MIMO, MEC, etc.

Guang. Chen received the B.S. degree from Uni- versity of Science and Technology Beijing, in 2018. He is currently pursuing the Ph.D. degree with the School of Computer and Communication Engineer- ing, University of Science and Technology Beijing, China. His research interests include mobile edge computing, game theory, convex optimization.

Meijie. Yang received the B.S. degrees in Univer- sity of Science and Technology Beijing, China, in 2016. She is currently pursuing the Ph.D. degree in University of Science and Technology Beijing, China. Her research interests are mostly focused on physical layer, advanced waveforms techniques and signal processing for 5G systems.

Liping. Du Liping Du, received her B.Eng. and MA.Sc degree from Zhengzhou University, P.R. China, in 1998 and 2001, and her Ph.D from the Department of Electrical Engineering, Beijing Insti- tute of Technology, P.R. China, in 2005. From 2005 to 2006, she worked as a Research Associate in the Department of Electrical Engineering, City Univer- sity of Hongkong, Hongkong, under the supervision of IEEE Fellow Hong Yan. In 2006, she joined the Department of Communication, University of Sci- ence and Technology Beijing. From 2014 to 2015, she visited the CRES Lab of the University of California, Los Angeles. Now She is currently with the School of Computer Communication Engineering, University of Science and Technology Beijing as an associate professor. Her research interest covers wireless communication, signal processing, cognitive radio.

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