To support the explosive growth of Information and Communications Technology (ICT), Mobile Edge Computing (MEC) provides users with low latency and high bandwidth service by offloading computational tasks to the network’s edge. However, resourceconstrained mobile devices still suffer from a capacity mismatch when faced with latencysensitive and computeintensive emerging applications. To address the difficulty of running computationally intensive applications on resourceconstrained clients, a model of the computation offloading problem in a network consisting of multiple mobile users and edge cloud servers is studied in this paper. Then a user benefit function
With the proliferation of various smart devices (e.g., smart homes, wearables, smartphones), the mobile data traffic generated by these emerging services has exploded [
Mobileedge Computing (MEC) is one of the most promising solutions [
For the limited coverage of edge servers, unmanned aerial vehicles (UAVs) have been employed to improve the connectivity of ground Internet of Things (IoT) devices due to their high altitude [
For the limited computing and communication resources, many scholars have started to study and design suitable offloading decisions and resource allocation schemes. This optimization problem is usually abstracted as a Mixed Integer Nonlinear Program (MINLP), a nonconvex NPhard problem. Since solving the optimal solution of this type of problem directly is difficult and impractical when the number of offloading tasks is too large, a large amount of literature has been devoted to this study. The typical approach is to decouple the problem into two subproblems, i.e., resource allocation and offloading decision, and then solve them using different algorithms. The most used algorithms are heuristics. However, these algorithms are often faced with a lack of convergence speed and stability. Zhao et al. [
This paper will study the problem of resource allocation and offloading decisions. We jointly considered the time delay and energy consumption to improve the users’ experience. Then an
We characterize the
The proposed GCAGA runs in three stages. First, the transmission power and computation resource for each possible matching strategy under the current offloading decisions is optimized. Then, the capacity bound of each server is calculated with the Gini coefficient. Finally, AGA is used to find the offloading decisions by iterative updating resource allocation and matching strategies to minimize system
Recently, scholars have carried out much research on optimizing the factors involved in the task offloading and resource allocation problem. In this section, some typical works will be reviewed and compared with the proposed scheme.
Rahimi et al. [
The latter literature is written based on a multiusermultiedge system, but some fail to consider the time delay and energy consumption jointly. A socially aware dynamic computation offloading scheme was proposed by Liu et al. [
Other studies have taken both the time delay and energy consumption into consideration. They addressed the problem in different ways. However, only a few could consider the users’ experience, while others added the time delay and the energy consumption directly with two weight factors. However, the time delay and energy consumption may not necessarily have the same unit or even magnitude. Xu et al. [
The review of previous research shows that heuristic algorithms have received much attention in the performance optimization of MEC systems. It can find the approximate optimal solution to the problem in a reasonable time. However, such algorithms also have some inherent defects: One is easy to fall into the dilemma of locally optimal solutions, and the other is due to the randomness of initial solution generation, which can lead to a long iteration time of the system. These two drawbacks may cause the slow convergence speed and poor stability of convergence results. The GA algorithm has a fast convergence speed and stability, but it often eliminates the current lowest fitness individual (even if the individual has a good genetic pattern), leading to getting stuck in a locally optimal solution. The simulated annealing algorithm (SAA) can dynamically adjust its search space with the iteration process, and escape the local optimal solution by increasing system entropy, which has strong optimization performance. However, due to the difficulty in grasping the downward trend of system entropy, it is difficult to ensure the convergence stability of SAA.
After reviewing the recent work,
Literature  Time delay  Energy consumption  User experience  Convergence performance 

[ 
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[ 
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Proposed scheme  √  √  √  √ 
Unlike the above research work, we propose a userbenefit function
Consider a multiuser, multiserver MEC system, as shown in
Name  Description 

Set of users  
Set of MEC servers  
Subbands of MEC servers  
The total bandwidth of a MEC server  
The computing task for user 

The input data size of the task 

The workload of completing the task 

Uplink channel gain between user 

SINR from user 

The uplink transmission rate of user 

Coband interference density of server 

Background noise variance  
The transmission power of user 

The maximum transmission power of user 

Maximum computing resource of server 

The local computing power of user 

Computing resources allocated by the server 

Task offloading indicator  
Energy factor of the chip  
Crossover possibility  
Mutation possibility  
Maximum population  
Maximum number of iterations 
Assuming that each user
The local computing power of user
Meanwhile, the energy consumption of
Orthogonal Frequency Division Multiple Access (OFDMA) is used as a multiple access scheme in the uplink [
Define
Obviously, if the task of user
Thus, by Shannon’s theorem, the rate at which the user can send data to the MEC server is limited to
Therefore, the transmission time when the user sends its task input data in the uplink is
At this point, the energy the corresponding user consumes to send data is denoted by
Define
When the computational resource allocation decision is known, the execution time of task
In this section, the problem is described formally based on the above system model. Then the problem is decoupled into two continuoustype extreme value problems and a discrete integer programming problem. Finally, we will give the complete offloading strategy.
The user experience is used as the benefit evaluation criterion for resource allocation and offloading decisions. Since the time delay and energy consumption may not necessarily have the same unit or even magnitude, it is more reasonable that the experience of users is mainly characterized by the relative improvement in task completion time and energy consumption in a mobile cloud computing system [
The target is to maximize
In problem
In this section, we transform the highcomplexity joint optimization problem into an equivalent master problem and a set of lowcomplexity subproblems.
First, the constraints on the resource allocation and offloading decisions are decoupled from each other, so with the offloading decision
After replacing the corresponding parts of
Observing
As a result, the optimal resource allocation scheme
The first term on the lefthand side in
However, since the transmit power of different users in the MEC system is independent, the above equation can also be decomposed into an optimal transmit power problem for each user. The function of
It is easy to see that when
The derivative for
For
The second term of
where
Ref. [
For a fixed task offloading strategy, it is possible to determine the resource allocation strategy
Since there is only one optimization variable
We define
Define the revenue function for server
Thus, we obtain the capacity bound
The detailed procedure of the preoffloading and capacity estimation is shown in Algorithm 1. The preoffloading part requires all possible binary groups
In the practical application scenarios of MEC networks, the number of servers
To evaluate the generalizability of the algorithm, we need to consider whether the algorithm depends on specific data distributions or assumptions. In Algorithm 1, we utilize the preoffloading operation to obtain the load capacity of each server, which indicates that Algorithm 1 relies on certain prior knowledge. Therefore, Algorithm 1 is only applicable to MEC networks with global controllers.
With
where
For
The fitness function is given by
The penalty is not applied to
The parameters include the crossover probability
The detailed procedure of GCAGA is shown as Algorithm 2. The time complexity of the external circulation of GCAGA is
In this section, appropriate data are provided for the experiment. To prove the effectiveness of adaptive heuristic operators and the Gini coefficientbased optimization strategy, an ablation study is employed and the comparison groups are set in
Name  Gini coefficient  Adaptive operators  GA 

GA  ×  ×  √ 
AGA  ×  √  √ 
GCAGA  √  √  √ 
We will verify the effectiveness of Algorithms 1 and 2 from three aspects, i.e., convergence behavior, convergence results, and convergence speed. We will triple mean filter the data to make the experimental curves easier to analyze.
The parameters are set as shown in
Parameter  Value 

100 MHz  
0.1 W  
5 MHz  
[5, 40] MHz  
−100 dBm  
10 MB  
10^{−11}  
(0, 2]  
0.05  
0.4  
64  
100 
To evaluate the convergence behavior of the three algorithms, we conducted 100 repeated experiments for each of them, with 95% Confidence Interval (CI). The corresponding parameters are set as
As can be seen from
As shown in
Notice that in
As shown in
As shown in
In
In summary, in the simulation experiments in
From
In
In
To conclude,
Experimental analysis shows that the proposed Gini coefficientbased offloading strategy can reduce the size of the solution space and adaptively converge, making it effective for realworld MEC networks. Taking the widely used MQTT (Message Queuing Telemetry Transport) protocol of IoT as an example, both QoS 1 and QoS 2 services have reply messages from MEC servers, ensuring that
This paper studies the resource allocation and computational offloading problem in a multiuser multiserver MEC system. First, the offloading benefit of each user is modeled as a weighted sum of latency and energy improvement ratios. Then the total sum of offloading benefits
The resources and computing environment was provided by the Xi’an Shiyou University, Xi’an, China. We are thankful for their support.
The authors received no specific funding for this study.
Study conception and design: Qiuchao Dai, Junqing Bai; data collection: Yingying Li; analysis and interpretation of results: Qiuchao Dai, Yingying Li; draft manuscript preparation: Qiuchao Dai, Junqing Bai. All authors reviewed the results and approved the final version of the manuscript.
All data generated or analyzed during this study are included in this published article.
The authors declare that they have no conflicts of interest to report regarding the present study.