2.1

Scene description

The mobile edge computing scenario in this paper consists of multiple mobile devices and a MEC edge cloud. Assume that the number of mobile devices is N, the number of computing tasks is I, user N = {1, 2, …, n}, and task I = {1, 2, …, i}. After the user sends the task request, the mobile device can connect with the edge cloud through the wireless channel. For task U_n,i of mobile devices, it can be defined by binary groups (i.e., U_n,I = {C_i d_i }), where C_i is the number of computing resources required to complete task I, that is, the total number of CPU cycles, and d_i is the data volume of task I, in bit.

2.2

Time delay model

Different devices will cause different delays when running tasks. This section considers two situations, namely, the current task is carried out locally and the task is offloaded. The delays involved in the above situations include: local computing delay, data uploading delay of mobile devices, computing delay of MEC server, and feedback delay, which can be ignored because the feedback delay is far less than the uploading delay.

2.3

Energy consumption model

2.4

Problem formalization

For the task caching problem, a decision variable X1_i ∈ {0,1} can be defined. When X1_i = 1, it means that the task I is cached to the edge cloud for execution; if the value is 0, it means that the task is not cached. In this case, only the delay of task execution in the edge cloud needs to be considered. There is an edge cloud cache resource constraint, that is, the total amount of cached task data must be smaller than the edge cloud cache size. For the task offload problem, the unloading ratio can be defined as X2_i. ∈[0,1]. When X2_i. = 0, tasks are executed locally; when X2_i. = 1, all tasks are unloaded to the edge cloud; when X2_i ∈(0,1), part of tasks are unloaded to the edge cloud and the rest are executed locally.

To sum up, the total delay can be obtained as follows:

Total energy consumption of mobile devices:

The objective of the algorithm is to find the unload ratio and cache decision with the minimum delay of the system under the constraint of the maximum energy consumption of edge cloud resources and mobile devices. Therefore, the problem can be formalized as:

The objective function means that the delay cost of the system is minimized through the task cache and the decision on the unloading ratio. Among them, constraint C1 indicates that the total amount of data for caching tasks cannot be greater than the caching capacity of the edge cloud, constraint C2 indicates that the task caching decision variables are binary variables, and 1 and 0 represent caching or not respectively, constraint C3 indicates that some divisible tasks are executed locally while the rest are executed on the edge cloud, and constraint C4 indicates that the power consumption of mobile devices should be controlled within the maximum power consumption constraint.

3.1

Particle coding

Individual particles are encoded in floating point numbers. Each particle element can take any floating-point number between 0 and 1.0001. The dimension of particle coding is the same as the total number of tasks. If the particle element value pop = 1.0001, it indicates that the task is cached to the edge cloud, and pop ∈ [0,1] indicates that the value is the unloading ratio. The particle velocity represents how fast the task unloaded to the edge cloud, denoted as V = {v₁,v₂,…,v_i}. The particle velocity is initialized as a random floating-point number from -0.1 to 0.1, and the dimension encoded by the particle velocity should also be the same as the total number of tasks. The optimal position of each particle in the evolutionary iteration process is G_best, and the optimal position of all particles is Z_best, which is the allocation method that minimizes the cost of the system.

3.2

Fitness function

Particle fitness represents the total delay cost of the system when the unloading decision and cache decision are adopted, and the function is as follows:

3.3

Algorithm flow

For equation (10), that is, the minimization of the objective function, the unloading strategy based on GA-PSO with caching mechanism can be used to solve it.

The main process of the algorithm:

4.1

Simulation environment

In this section, an edge computing system composed of edge cloud and mobile devices is constructed by Matlab, and the unloading strategy based on GA-PSO and cache mechanism is implemented, and the performance of the strategy is evaluated in detail. Experimental parameters are shown in Table 1.

Table 1.

Simulation parameters.

4.2

Analysis of results

Figure 2 shows the comparison of the system delay cost of local computing and offloading all tasks to the MEC server, based on the GA-PSO algorithm without a caching mechanism, and an offloading strategy with a caching mechanism under different numbers of devices. It can be observed that the total system delay of the three types of strategies when the number of devices is 25, 50, 75, 100, 125, and as the number of devices increases, the delays of these four types of strategies are all showing an increasing trend, but the strategy in this article The system delay is less than the delay of the other three schemes.

Figure 2.

Impact of number of devices on delay.

Figure 3 shows the relationship between edge cloud cache capacity, energy consumption of mobile devices and total system delay when GA-PSO unloading strategy, local computing and all tasks are unloaded to MEC server in this paper. The left ordinate is equipment power consumption, and the right ordinate is system delay. As can be seen from Figure 3, with the increase of cache resources, energy consumption tends to decrease, that is, the more task data that edge cloud can cache, the lower the energy consumption of mobile devices will be. In addition, the energy consumption of local computing is significantly higher than that of this strategy, indicating that the GA-PSO unloading strategy in this paper reduces the energy consumption of mobile devices to a certain extent, because the relevant data of some tasks have been cached in the edge cloud, and the execution of such tasks has no energy consumption for mobile devices. It can also be seen from Figure 3 that the larger the edge cloud cache capacity is, the smaller the system delay is, indicating that cache has a great impact on the delay. This is because the larger the cache capacity is, the more cacheable tasks are, and the execution time of cached tasks is shorter than that of non-cached tasks that need to be unloaded.

Figure 3.

Impact of edge cloud caching capability on delay and power consumption.