Keywords

1 Introduction

With the rapid development and popularization of mobile Internet and the Internet of things (IoT), various applications such as augmented reality (AR) and virtual reality (VR) has greatly expanded the functions of mobile devices. Meanwhile, IoT businesses such as smart city, environmental monitoring, and intelligent agriculture are emerging. However, due to the limited storage, computing and perceived capabilities of mobile devices, mobile applications face many challenges in quality of service (QoS), mobility management and security. In this case, a new computing paradigm, i.e. Mobile Edge Computing (MEC), has been paid much attention by researchers due to its wide employment in several scenarios, such as IoT and Vehicular Network.

A typical mobile edge computing architecture consists of MEC servers and mobile devices [1, 2]. Compared to mobile devices, MEC servers are deployed at the edge of the network and have more available resources, which can process some computation-intensive, storage-intensive or latency tolerant tasks. And mobile devices can reduce their own computing load and energy consumption by offloading some tasks to MEC servers. Therefore, it is very important to design an efficient task scheduling strategy under MEC architecture. Previous works have investigated heuristic algorithms to deal with scheduling problem in MEC such as genetic algorithm and ant colony optimization (ACO) algorithm. However, traditional heuristic algorithms have some shortcomings such as high complexity, long iteration time and local optimum. When a large number of tasks need to be processed, the traditional scheduling algorithm is used to iterate for too long and cannot meet the requirements of tasks’ deadline, which affecting mobile device user’s quality of experience (QoE). Moreover, When the traditional task scheduling algorithm selects the resource, its target is the total service resource, which does not consider the characteristics of the resource itself and the preferences of the user or task, which leads to the large cost of the resource selection and the blind interest. Therefore, it is important to find a suitable method to reduce the resource selection range, thereby reducing the task scheduling spending.

Inspired by the above motivations, an ant colony optimization and fuzzy clustering (ACOFC) algorithm is proposed in this paper. Firstly, according to the tasks’ preference for resources, the fuzzy clustering algorithm is used to divide the resources in order to reduce the space of the resource search and the complexity of the algorithm. Afterwards, the ACO algorithm is used to find the optimal scheduling solution in the divided spaces. At last, a series of numerical tests are conducted to illustrate the performance of the ACOFC algorithm is better than that of the First-Come-First-Served algorithm (FCFS) and the ACO algorithm.

The rest of paper is organized as follow. Section 2 overviews related studies on task scheduling. the system model is presented and, the joint scheduling problem is formulated in Sect. 3. The calculations of collision probability and access delay are discussed in Sect. 4. Section 5 presents a series of numerical test. Finally, the contributions of this paper are concluded in Sect. 6.

2 Related Work

In the previous work, Wei et al. formulated the joint scheduling problem as a 0-1 knapsack problem for the deadline-constraint tasks and the ACO-based method was employed to maximize the profits for the service providers [3]. In [4], They put forward a scheduling algorithm based on MAX–MIN Ant System (MMAS) considering multi-dimensional resources. Then, the load balancing of mobile devices was considered when scheduling the results [5]. Later, Wang et al. modified the algorithm while taking the types of tasks with deadline-constraint into consideration [6].

Although amounts of heuristic traditional scheduling algorithms have been proposed to scheduling problems with different targets, how to improve the traditional algorithm to solve scheduling problem is rarely studied in the MEC system. In [9], Wang et al. proposed an improved genetic algorithm method where the min-min and max-min algorithm are used to boost the search efficiency. For improving ACO algorithm’s shortcomings in task scheduling, a task scheduling algorithm based on simulated annealing ant colony Algorithm is put forward in [10]. In this algorithm, the local optimal solution is constructed by ACO algorithm, the strong local search ability of simulated annealing algorithm (SA) is utilized to avoid algorithm trapped in local optimum at a certain probability.

3 System Model and Problem Formulation

3.1 MEC System Model

Before introducing the scheduling problem, our system model is presented in Fig. 1. The service providers, including MEC servers and mobile devices, can run the tasks concurrently. MEC servers are attached to the access point of the mobile devices to achieve low response latency, and mobile devices can offload tasks to the mobile servers. Both mobile devices and MEC servers have limited resources. MEC servers have more available resources than mobile device so that the processing time for task on MEC servers is shorter. Assume that each task cannot be further partitioned. The general working process is as follow:

Fig. 1.
figure 1

System model

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  • Each mobile device sends offloading requests to the decision maker in MEC servers by the wireless access network.

  • According to the collected offloading requests of all the mobile devices and the property of each task, the decision maker executes the scheduling algorithm to decide where should the tasks be processed (in the mobile device locally or in the MEC server).

  • The mobile devices offload the chosen tasks to the MEC servers.

  • The MEC servers handle the tasks received and send their results to the mobile devices.

3.2 Problem Formulation

Assume that the resource dimension is three dimensions the resource for each MEC server i can be represented as a vector \( \overrightarrow {c}_{i} = (c_{i}^{comp} ,c_{i}^{stor} ,c_{i}^{comm} ) \), where c comp i , c stor i and c comm i represents computing resources, storage resources and communication resources respectively. The set of tasks to be scheduled is represented as \( I = \{ 1,2, \ldots ,n\} \), the value of each task in I is expressed as \( (p_{1} ,p_{2} , \ldots ,p_{n} ) \). And when the task i is running on the MEC server j, the resource that it consumes is represented as a vector \( \overrightarrow {{r_{ij} }} = (r_{ij}^{comp} ,r_{ij}^{stor} ,r_{ij}^{comm} ) \). Assuming that all the task scheduling requests reach the decision maker at the same time and each task can only be offloaded to one MEC server. Under the constraints of the resources of each MEC server, the scheduling goal is to maximize the total profits, namely:

$$ {\text{Maximize}}\sum\limits_{j = 1}^{n} {\sum\limits_{i = 1}^{m} {p_{j} \times x_{ij} } } $$
(1)
$$ {\text{Subject}}\,{\text{to}}:\sum\limits_{j = 1}^{n} {x_{ij} } \le 1,\;i = 1,2, \ldots ,m $$
(2)
$$ \sum\limits_{i = 1}^{m} {\overrightarrow {{r_{ij} }} \times x_{ij} } \le \overrightarrow {{c_{i} }} ,\;j = 1,2, \ldots ,n $$
(3)
$$ x_{ij} \in \left\{ {0,1} \right\},\;i = 1,2, \ldots ,m;j = 1,2, \ldots ,n $$
(4)

From the above scheduling problem, we can see that this is a three-dimensional 0-1knapsack problem, and is NP-hard.

4 Tasks Scheduling Algorithm

The simple ACO algorithm has the advantages of parallelism, synergism and positive feedback, but when solving the complex NP-hard problem of task scheduling, the algorithm has some shortcomings such as poor local search ability, easy to fall into the local optimal solution and slow convergence speed.

For solving this NP-hard scheduling problem, we propose an ACOFC algorithm, which can be widely utilized to solve this kind of combinational optimization problem. At first, fuzzy clustering algorithm is used to divide the tasks to be scheduled can be divided into three categories by tasks’ preference for resources: computational task set, bandwidth task set, and storage task set. Similarly, MEC servers can be divided into three categories: computational server set, bandwidth server set and storage server set. By using fuzzy clustering algorithm, the tasks and the MEC servers are divided respectively, which reduces the spatial space of the search and the complexity of the algorithm. Afterwards, Because of the strong global search ability of ACO algorithm, the ACO algorithm is used to find the optimal scheduling solution in the space of task set and MEC server set with the same resource preference.

4.1 Resource Fuzzy Clustering

Fuzzy c-means clustering method (FCM) is a data clustering method based on the optimization of objective function. Given the data set X = {x1, x2, …, xn}, the objective of FCM algorithm is to find a fuzzy partition cluster Uc×n of the data set, that is, divide the original data into c fuzzy groups, and minimize the non-similarity index between each group of samples and its clustering center. The general definition of clustering objective function is as follows.

$$ J(U,c_{1} , \cdots ,c_{c} ) = \sum\limits_{i = 1}^{c} {J_{i} } = \sum\limits_{i = 1}^{c} {\sum\limits_{j}^{n} {u_{ij}^{a} } } d_{ij}^{2} $$
(5)

where Uij represents the membership degree of data j to fuzzy group i, the value of Uij is between 0 and 1. ci is the clustering center of fuzzy group i, and \( d_{ij} = ||c_{i} - x_{j} || \) is the Euclidean distance between the i clustering center and the j data point. \( {\text{a}} \in [1,\infty ) \) is a weighted index.

4.2 ACO Tasks Scheduling Algorithm

After fuzzy clustering of tasks and MEC servers, the task set and MEC server set, which have the same resource preferences, are respectively taken as tasks to be scheduled and service providers for ACO algorithm.

The basic principle of ACO algorithm is to release pheromones on the path of the natural ants, and the following the concentration of the remaining pheromones in the path of the left pheromones is higher, and the higher the concentration of the remaining pheromones, the greater the probability of selecting the path, which gradually converts to the process of the optimal solution of the entire company.

Local Heuristic Information and Path Selection.

In the ACO algorithm, the path can be determined by pheromone concentration and local heuristic values. Resource consumption is an important factor influencing the scheduling goals. Therefore, the local heuristic value can be determined by the remaining resources. This means that the corresponding path of a host with a larger remaining resource has a higher priority. ACOFC algorithm considers the task profit and the resource consumption of the task, and defines the local heuristic information as

$$ \eta_{i} (t) = \frac{{h_{i} }}{{\sum\limits_{j = 1}^{m} { |\frac{{\overrightarrow {{c_{i} }} }}{{\overrightarrow {{c_{i} }} - \overrightarrow {{r_{ij} }} }} |} }} $$
(6)

where hi represents the profit of task i. And the probability that ant q selects the next task i is

$$ P_{ij}^{q} = \left\{ {\begin{array}{*{20}c} {\frac{{\left[ {\tau_{ij} (t)} \right]^{\alpha } \left[ {\eta_{ij} (t)} \right]^{\beta } }}{{\sum\nolimits_{k \in allowedq(t)} {\left[ {\tau_{ik} (t)} \right]^{\alpha } \left[ {\eta_{ik} (t)} \right]^{\beta } } }}} \\ {0,\;\quad \quad \quad \quad \quad otherwise} \\ \end{array} } \right. $$
(7)

where \( \alpha \) and \( \beta \) are the weighted factors of the pheromone and heuristic value. \( \tau_{ij} (t) \) presents the pheromone concentration on the path from i to j at time t.

Pheromone Update.

After each cycle of ACO algorithm, the pheromone needs to be updated according to the partial solutions. At first, the pheromone applied on the link would decline at a certain rate according to the volatile characteristics of pheromone. Besides, the solutions will increase its value for the ants. Assume that \( \tau_{ij} (t) \) will be updated to be \( \tau_{ij} (t + 1) \) at time t +1.

$$ \tau_{ij} (t + 1) = (1 - \rho )\tau_{ij} (t) + \Delta \tau_{ij} (t) $$
(8)

where \( \rho \) represents the evaporation rate of the ant. \( \Delta \tau_{i} (t) \) is the increment of the pheromone, which can be determined according to the partial solution. The calculation of \( \Delta \tau_{j} (t) \) is:

$$ \Delta \tau_{ij} (t) = \sum\nolimits_{q = 1}^{Q} {\Delta \tau_{ij}^{q} (t)} $$
(9)

where Q is the ants’ number. \( \Delta \tau_{ij}^{q} (t) \) is determined by the partial solution at time t:

4.3 Algorithm Description

figure a

5 Numerical Tests

In this section, we conduct a series of numerical tests to analyze the ACOFC algorithm by MATLAB simulator. In order to better evaluate the performance of the ACO algorithm, two typical scheduling algorithms, i.e. FCFS algorithm and ACO algorithm are utilized to compare with our proposed algorithm under different experimental settings.

In this simulation, the dimension of the resource is three, which represents computing resources, communication resources, and storage resources. There are m MEC servers and n tasks in the MEC system. Assume that these tasks arrive at the same time and each task has a large demand for a certain resource. The task’s consumption of three-dimensional resources is in the range [a1, a2] on a MEC server. And the three-dimensional resource capacity of MEC servers is evenly distributed within the interval [a3, a4]. The profit of the task is subject to uniform distribution [a5, a6] within the interval. The number of loops is set to 5. The main parameters employed in the simulation process are illustrated in Table 1.

Table 1. Related parameters
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Figure 2 shows the impact of \( \beta \), which is defined as the local heuristic value in the path section process, on the result of ACOFC algorithm. The x-coordinates are the \( \beta \), and the y-coordinates are the total profit. As \( \beta \) increases, the total profit increases with it linearly. While total profit is little reduced when \( \beta \) is larger than 5.

Fig. 2.
figure 2

Comparison of total profit for different \( \beta \)

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The performance of ACOFC algorithm is illustrated in Fig. 3. by comparing with ACO algorithm and FCFS algorithm. the x-coordinate represents the cycles and the y-coordinate represents the total profit. From the figure, we can see that the total profit of ACOFC algorithm is close to that of ACO algorithm.

Fig. 3.
figure 3

The total profit varies with cycle for ACO, ACPFC and FCFS

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In Fig. 4, the x-coordinates are the number of tasks, and the y-coordinates are the run time. We compare the run time of ACPFC algorithm with that of ACO algorithm under different number of tasks. We can see that the running time of ACOFC algorithm is much shorter than ACO algorithm, especially in the case of a large number of tasks to be scheduled

Fig. 4.
figure 4

Comparison of run time for different number of tasks

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6 Conclusion

In this paper, by combining the ACO algorithm and the fuzzy clustering algorithm, we have proposed an ant colony optimization fuzzy clustering algorithm to deal with a NP-hard scheduling problem. At first, according to the tasks’ preference for resources, fuzzy clustering algorithm is used to divide the resources in order to reduce the space of the resource search and the complexity of the algorithm. Afterwards, the ACO algorithm is used to find the optimal scheduling solution in the divided spaces. At last, a series of numerical tests are conducted to illustrate the performance of the ant colony optimization fuzzy clustering algorithm is better than that of the FCFS algorithm and the ACO algorithm.