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A new load balancing strategy by task allocation in edge computing based on intermediary nodes

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Abstract

The latency of cloud computing is high for the reason that it is far from terminal users. Edge computing can transfer computing from the center to the network edge. However, the problem of load balancing among different edge nodes still needs to be solved. In this paper, we propose a load balancing strategy by task allocation in edge computing based on intermediary nodes. The intermediary node is used to monitor the global information to obtain the real-time attributes of the edge nodes and complete the classification evaluation. First, edge nodes can be classified to three categories (light-load, normal-load, and heavy-load), according to their inherent attributes and real-time attributes. Then, we propose a task assignment model and allocate new tasks to the relatively lightest load node. Experiments show that our method can balance load among edge nodes and reduce the completion time of tasks.

Introduction

The Internet of Things (IoT) can connect a large number of smart devices across regions and it has become part of many advanced application infrastructures. It also generates large amounts of data, which will keep on growing in the coming years[1, 2]. However, the limitations of its devices make it very complicated to solve current paradigms such as big data or deep learning [3]. In the last few years, the integration of the IoT with disruptive technologies such as cloud computing has provided the capabilities needed in the IoT to address these paradigms[4]. The advent of cloud computing technology has provided us with a light-weight resolution for building various complex business applications[5]. However, cloud computing centers are usually located far away from mobile users, and data delays between users and remote clouds might be long and unpredictable. And users accessing the remote cloud can result in high access latency, which can seriously affect network performance[6].

Edge computing is slowly moving cloud computing applications, data and services from centralized nodes to the edge of the network[7]. And it is located between terminal devices and traditional cloud computing data centers for handling low latency and real-time tasks [8]. This service is seen as a cloud close to the end user to provide computing and services with less latency[9].

Although edge computing can greatly reduce latency, the unreasonable assignment of tasks leads to the unbalanced load of each node [10]. And because of the diversity and heterogeneity of edge computing nodes, the general load balancing algorithm can not be directly applied to edge computing. Therefore, edge computing load balancing has become a very important research topic in academia.

There are two main types of load balancing strategies: static and dynamic. Static load balancing algorithms do not consider the previous state of the node, while distributing the load and it works well when nodes have a small variation in the load. So it is not suitable for edge environment. Load balancing strategy by task allocation in edge computing based on intermediary nodes is a dynamic load balancing technique, which considers the previous state of a node while distributing the load[11].

In this paper, we propose a network architecture for edge computing based on the intermediary node to better obtain the state information of the node. The intermediary node classifies and evaluates the status of the node by using the intrinsic attribute values and the real-time attribute values. And return the node information with the relatively lightest result. Then we propose a task allocation model that the relatively lightest nodes and the task arrival node are used as the target node to allocate new tasks, while the other nodes are not assigned tasks temporarily, so as to achieve dynamic balancing of the system. The main contribution of this paper can be summarized as follows:

  1. 1.

    We studied the load balancing strategy in the edge computing environment and implemented dynamic load balancing through task allocation. We propose an edge computing network architecture based on intermediary nodes. Compared with the traditional architecture, this architecture adds intermediary nodes in the edge computing layer and cloud computing layer to better control the global information of the edge nodes.

  2. 2.

    For the system with unbalanced initial state, we use naive Bayes algorithm to classify the state of nodes. And standardize the original data in order to avoid highlighting the role of higher-value indicators in the comprehensive analysis when the levels between the indicators vary greatly. And we take the nodes with relatively light classification state and the nodes of task arrival as the target nodes to allocate new tasks, while the other nodes are not assigned tasks temporarily, so as to achieve dynamic balancing.

  3. 3.

    A mathematical framework is cast to investigate the load balancing problem between edge nodes. The purpose of load balancing is achieved by the method of task assignment and estimating the task completion time based on the transmission rate between edge nodes, the computation speed, and the current tasks calculation time.

The rest of the paper is organized as follows. Section 2 reviews the related work in edge computing and load balancing. Section 3 describes the load balancing strategy, including the selection of target nodes and the task allocation model. The simulation results and analysis are presented in Section 4. Finally, Section 5 draws a conclusion.

Related work

Edge computing optimizes cloud computing systems by performing data processing at the edge of the network closest to the data source using the concept of caching and data compression. Due to the proximity to the end users, low latency, and other advantages, the research on edge computing has attracted great attention with a large quantity of literature. In this section, we review the research progress of edge computing and load balancing.

In the work of He et al. [12], an improved constrained particle swarm optimization algorithm based on software-defined network (SDN) is proposed in the framework of software-defined cloud-fog network. This algorithm improves the performance of the algorithm by using the opposite property of the mutated particles and reducing the inertia weight linearly. Chen et al. [13], proposed a task allocation model to solve the load balancing at the server level. Calculate the completion time of the large aggregation tasks on each server by treating the tasks offloaded by other servers as one large aggregation task. They formulate a load balancing optimization problem for minimizing deadline misses and total runtime for connected car systems in fog computing.

In the work of Wang et al. [14], a distributed city-wide traffic management system is constructed. And design an offloading algorithm for real-time traffic management in fog-based internet of vehicle (IoV) systems, with the purpose of minimizing the average response time of the traffic management server (TMS) for messages. Ning et al. [15], investigated a joint computation offloading, power allocation, and channel assignment (COPACA) scheme for 5G-enabled traffic management systems, with the purpose of maximizing the achievable sum rate. In the work of Ning et al. [16], in order to satisfy heterogeneous requirements of communication, computation and storage in IoVs, they constructed an energy-efficient scheduling framework for MEC-enabled IoVs to minimize the energy consumption of road side units (RSUs) under task latency constraints. Ning et al. [17], proposed a deep learning based data transmission scheme by exploring trirelationships among vehicles at the edge of networks (i.e., edge of vehicles) by jointly considering the social and physical characteristics. In the work of Ning et al. [18] a deep reinforcement learning (DRL) method is integrated with vehicular edge computing to solve the computation ofoading problem, where we jointly study the optimization of task scheduling and resource allocation in vehicular networks.

Our team has done a lot of work on edge computing and fog computing. For example, the resource scheduling method for fog computing is studied [19], the data processing delay optimization in mobile edge computing [20], and the resource scheduling in edge computing[21], etc. In this paper, We focus on the load balancing problem of edge computing. In our research, for the system with unbalanced initial state, we propose a load balancing strategy by task allocation in edge computing based on intermediary nodes. First, the state of nodes is classified and evaluated according to their inherent and real-time attributes. Then, according to the classification results, the target nodes are selected. Finally, the new task assignment is completed according to the task assignment model proposed by us.

Load balancing strategy

In this paper, we will study the load balancing technology under the edge computing architecture based on intermediary nodes. The network model of this architecture is shown in Fig. 1.

Fig. 1
figure1

Network architecture of edge computing based on mediation nodes

In this architecture, we store the intrinsic attributes of the node to the intermediary node before applying the load balancing strategy. When a new task arrives at a node, this node sends a request signal to the intermediary node. The intermediary node is responsible for forwarding the signal to the edge node and the edge node that received the signal returns its real-time properties values. After receiving the real-time attribute, the intermediary node starts classification of the edge node.

Selection of target nodes

Selection of load attributes

There are many factors affecting load balancing, including memory, CPU, disk and network bandwidth. However, it is incomplete to judge the load state of nodes by ignoring one or several factors. In our research, we will evaluate the state of nodes by combining the intrinsic and real-time attributes of nodes. Intrinsic and real-time properties are defined as follows [22]:

Definition 1

Intrinsic attributes. Static properties of the nodes, including physical memory, CPU main frequency multiplied by the number of cores, disk size, and network bandwidth.

Definition 2

Real-time attributes. Dynamic attributes of nodes, that is, attribute values monitored by the intermediary node in real time, including memory usage, disk usage, CPU utilization, and bandwidth utilization.

When the levels between the indicators vary greatly, if we directly use the original index value for analysis it will highlight the role of higher-value indicators in the comprehensive analysis and relatively weaken the role of lower-value indicators [22]. So we perform dimensionless processing of the intrinsic attributes, and each attribute value of node i is represented as:

Definition 3

The values of load attribute [23]. The combination of intrinsic and real-time attributes of edge node i is used as a criterion for classifying load states of nodes. Expressed as L=(L1,L2,L3,L4), and each attribute value of node i is represented as:

The property values of memory: \(L_{1}=\sigma _{1}R_{i}^{1}+\sigma _{2}\left (1-R_{i}^{2}\right)\), where \(R_{i}^{1}\) is the size of physical memory after dimensionless processing, and \(R_{i}^{1}=\frac {R_{i}-\min (R_{i})}{\max (R_{i})-\min (R_{i})}\), Ri represents the memory size of node i. \(R_{i}^{2}\) is the memory utilization of node i. And σ1+σ2=1.

The property values of CPU: \(L_{2}=\varepsilon _{1}C_{i}^{1}+\varepsilon _{2}\left (1-C_{i}^{2}\right)\), where \(C_{i}^{1}\) the product of the CPU main frequency and core number after dimensionless processing, and \(C_{i}^{1}=\frac {C_{i}-\min (C_{i})}{\max (C_{i})-\min (C_{i})}\), Ci represents the product of the CPU main frequency and core number of nodes i. \(C_{i}^{2}\) is the CPU utilization of node i. And ε1+ε2=1.

The property values of disks: \(L_{3}=\delta _{1}D_{i}^{1}+\delta _{2}\left (1-D_{i}^{2}\right)\), where \(D_{i}^{1}\) is the size of disks after dimensionless processing, and \(D_{i}^{1}=\frac {D_{i}-\min (D_{i})}{\max (D_{i})-\min (D_{i})}\), Di represents the disks size of nodes i. \(D_{i}^{2}\) is the disks utilization of node i. And δ1+δ2=1.

The property values of bandwidth: \(L_{4}=\omega _{1}B_{i}^{1}+\omega _{2}\left (1-B_{i}^{2}\right)\), where \(B_{i}^{1}\) is the size of bandwidth after dimensionless processing, and \(B_{i}^{1}=\frac {B_{i}-\min (B_{i})}{\max (D_{i})-\min (B_{i})}\), Bi represents the bandwidth size of nodes i. \(B_{i}^{2}\) is the bandwidth utilization of node i. And ω1+ω2=1.

Definition 4

Sample classification set: T={Tj|j=1,2,3}, T1 represents the light-load state, T2 represents the normal-load state, and T3 represents the heavy-load state.

Classification of node states

In this section, we use the load attribute value as a basis to classify the state of the node by the Naive Bayes algorithm. Based on Bayesian theory, this classification method is a pattern recognition method with known prior probability and conditional probability [24]. According to Bayesian theorem, when each attribute is independent of each other, its classification result is the most accurate. The selected attributes of us are actually independent between each other and thus meet the condition of it. Let the sample space be U and the prior probability of training sample classification Tj be Pr(Tj)(j=1,2,3). Its value is equal to the total number of samples belonging to class Tj divided by the total number of training samples |U|. For an unknown sample nx, the conditional probability that it belongs to the Tj class is Pr(nx|Tj). According to Bayesian theorem, the posterior probability that it belongs to the Tj class is Pr(Tj|nx):

$$ Pr(T_{j}|n_{x})=\frac{Pr(n_{x}|T_{j})Pr(T_{j})}{Pr(n_{x})}. $$
(1)

Let the load attribute value \(L(n_{x})=\left (L_{1}^{n_{x}},L_{2}^{n_{x}},L_{3}^{n_{x}},L_{4}^{n_{x}}\right)\) of unknown sample nx, where \(L_{k}^{n_{x}}\) represents the kth attribute value of sample nx, because we assume that \(L_{k}^{n_{x}}(k=1,2,3,4)\) is independent of each other, the conditional probability of belonging to Tj is as follows:

$$ {}Pr(n_{x}|T_{j})\,=\,Pr(\!(L_{1}^{n_{x}},L_{2}^{n_{x}},L_{3}^{n_{x}},L_{4}^{n_{x}})|T_{j})\,=\,\prod_{k=1}^{4}Pr(L_{k}^{n_{x}}|T_{j}). $$
(2)

where \(Pr(L_{k}^{n_{x}}|T_{j})\) denotes the probability when the kth load attribute value of sample nx belong to Tj classification. From (1) and (2), the posterior probability of Tj is obtained as follows:

$$ Pr(T_{j}|n_{x})=\frac{Pr(T_{j})\ast\prod_{k=1}^{4}Pr(L_{k}^{n_{x}}|T_{j})}{Pr(n_{x})}. $$
(3)

According to the Naive Bayes classification method, the posterior probability multiplied by the prior probability maximum term is the class of the unknown sample nx, and it is represented by the following formula:

$$ \arg\max\{Pr(T_{j}|n_{x})Pr(T_{j})\}(j=1,2,3). $$
(4)

From the Eqs. (3) and (4), the classification decision function of sample nx is:

$$ \arg\max\{Pr(T_{j})^{2}\ast\prod_{k=1}^{4}Pr(L_{k}^{n_{x}}|T_{j})\}(j=1,2,3). $$
(5)

Therefore, the state of the sample can be represented by Eq. (6).

$$ {}T_{V_{x}}= \left\{ \begin{array}{ll} \text{light}-\text{load}, & \arg\max\left\{Pr\left(T_{j}\right)^{2}\ast\prod_{k=1}^{4}Pr\left(L_{k}^{n_{x}}|T_{j}\right)\right\}=1\\ \text{normal}-\text{load},& \arg\max\left\{Pr\left(T_{j}\right)^{2}\ast\prod_{k=1}^{4}Pr\left(L_{k}^{n_{x}}|T_{j}\right)\right\}=2\\ \text{heavy}-\text{load},& \arg\max\left\{Pr\left(T_{j}\right)^{2}\ast\prod_{k=1}^{4}Pr\left(L_{k}^{n_{x}}|T_{j}\right)\right\}=3 \end{array} \right. $$
(6)

According to the Eq. (6), when the predicted result of an unknown node state is 1, it represents that the current state of the node is light load state, and if the predicted result is 2, it indicates that the current state of the node is normal load state, otherwise it is heavy load state.

The intermediary node divides the edge nodes into three categories according to the above method, and returns the information of node with relatively light node status (the smallest classification result). This kind node is designated as the target node.

Task allocation model

When one or more tasks arrive at node ni simultaneously, these tasks are merged into an aggregated task U. And according to the information of the target node, the aggregated task is decomposed into several subtasks uj=αjU which are handled by different target nodes and the node which tasks arrived.

(1) The transmission time of task

The transmission time is the size of the subtasks divided by the data transmission rate from edge node ni to target node nj or cloud server d, that is:

$$ t_{1}=\frac{\alpha_{j}U}{B_{n_{i},n_{j}}}. $$
(7)
$$ t_{2}=\frac{\alpha_{d}U}{B_{n_{i},d}}. $$
(8)

Among them, \(B_{n_{i},n_{j}}\) is the data transfer rate of the edge node ni to the target node nj, and \(B_{n_{i},n_{j}}=\infty \) when ni=nj[11]. \(B_{n_{i},d}\) is the data transfer rate of the edge node ni to the cloud server d.

(2) The computation time of subtasks

$$ t_{3}=\frac{\alpha_{j}U}{f_{n_{j}}}+\tau_{n_{i},n_{j}}\frac{N_{n_{j}}}{f_{n_{j}}}. $$
(9)
$$ t_{4}=\frac{\alpha_{d}U}{f_{d}}+\tau_{n_{i},d}\frac{N_{d}}{f_{d}}. $$
(10)

Where, \(\frac {\alpha _{j}U}{f_{n_{j}}}\) is the calculation time of the subtask at the target node nj, and \(f_{n_{j}}\) is the computation speed of the target node nj. \(\tau _{n_{i},n_{j}}\frac {N_{n_{j}}}{f_{n_{j}}}\) is the current tasks calculation time of the target node nj. And \(\tau _{n_{i},n_{j}}=\lceil \alpha _{j}\rceil \), it denotes whether there is a task assignment relationship between the edge nodes ni and nj. \(\tau _{n_{i},n_{j}}=1\) denote that the relationship exists; \(\tau _{n_{i},n_{j}}=0\) indicates that the relationship does not exist [6]. \(N_{n_{j}}\) is the current task size of the target node nj. Similarly, we can get an explanation of the computation time t4 of subtasks in cloud servers.

(3) The transmission time of the computing result. In most cases, the computing result is a small packet such as a control signal; thus, the transmission time of the computing result can be ignored [25].

∙ The completion time of subtasks between edge nodes

$$ {}T_{1}(\alpha_{j})\,=\,\max(t_{1}+t_{3})=\max\left(\frac{\alpha_{j}U}{B_{n_{i},n_{j}}}+ \frac{\alpha_{j}U}{f_{n_{j}}}+\tau_{n_{i},n_{j}}\frac{N_{n_{j}}}{f_{n_{j}}}\right). $$
(11)

∙ The completion time of subtasks on cloud server

$$ T_{2}(\alpha_{d})=(t_{2}+t_{4})=\frac{\alpha_{d}U}{B_{n_{i},d}}+ \frac{\alpha_{d}U}{f_{d}}+\tau_{n_{i},d}\frac{N_{d}}{f_{d}}. $$
(12)

∙ Total completion time of aggregate task U

$$ {} \begin{aligned} T&(\alpha_{j},\alpha_{d})=\\ &\max\!\left\{\!\frac{\alpha_{j}U}{B_{n_{i},n_{j}}}\,+\, \frac{\alpha_{j}U}{f_{n_{j}}}\,+\, \tau_{n_{i},n_{j}}\frac{N_{n_{j}}}{f_{n_{j}}},\! \frac{\alpha_{d}U}{B_{n_{i},d}}\!+ \frac{\alpha_{d}U}{f_{d}}+\tau_{n_{i},d}\frac{N_{d}}{f_{d}}\right\}. \end{aligned} $$
(13)

In order to minimize the completion time, it is necessary to determine the optimal {αj,αd} set. In summary, the problem is modeled as follows:

$$ {} \begin{aligned} \min&\left\{\max\left\{\frac{\alpha_{j}U}{B_{n_{i},n_{j}}}+ \frac{\alpha_{j}U}{f_{n_{j}}} + \tau_{n_{i},n_{j}}\frac{N_{n_{j}}}{f_{n_{j}}}, \frac{\alpha_{d}U}{B_{n_{i},d}} + \frac{\alpha_{d}U}{f_{d}}\right.\right.\\ &\qquad\quad\left.\left.+\tau_{n_{i},d}\frac{N_{d}}{f_{d}}\right\}\right\}\\ {s.t.}&\sum_{j=1}^{k}(\alpha_{j}+\alpha_{d})=1 \end{aligned} $$
(14)

In this task model, the subtask assigned to each edge node satisfies uj=αjU. Therefore, the proportion of tasks allocated to target node and cloud can form a k+1 dimensional vector \(\alpha =(\alpha _{1}, \alpha _{2},...,\alpha _{k},\alpha _{k+1})^{\hat {o}}\) [12]. Assuming that the edge node n1 receives the current task, the total completion time T can be described as

$$ {}\begin{array}{ll} T(\alpha)=&\max\left(\frac{\alpha_{1}U}{B_{n_{1},n_{1}}}+ \frac{\alpha_{1}U}{f_{n_{1}}}+ \tau_{n_{1},n_{1}}\frac{N_{n_{1}}}{f_{n_{1}}},\dots,\right. \\ &\left.\frac{\alpha_{k}U}{B_{n_{1},n_{k}}}+ \frac{\alpha_{k}U}{f_{n_{k}}}+ \tau_{n_{1},n_{k}}\frac{N_{n_{k}}}{f_{n_{k}}}, \frac{\alpha_{d}U}{B_{n_{1},d}}+ \frac{\alpha_{d}U}{f_{d}}+\tau_{n_{1},d}\frac{N_{d}}{f_{d}}\right) \end{array} $$

Therefore, the mapping of the computing task is solved in the case where the aggregation task U is known, that is, the proportion of tasks assigned to each target node, the solution of vector α. In order to avoid overloading a node after being assigned a large number of tasks, we make the subtask u less than or equal to the average load of the system, that is \(u_{j}\leq \frac {\left (U+\sum _{j=1}^{k}N_{j}\right)}{m}\). Assuming that the total number of edge nodes is m, the problem can be reduced to the following optimization problems:

$$\begin{array}{@{}rcl@{}} &\alpha&=\underset{U\in I}{\arg}\min\{T(\alpha)\} \\ &{s.t.}&0\leq\alpha_{j}\leq1 \\ &&0\leq\alpha_{j}\leq1 \\ &&\alpha_{j}U\leq\frac{\left(U+\sum_{j=1}^{k}N_{j}\right)}{m} \\ &&\sum_{j=1}^{k}(\alpha_{j}+\alpha_{d})=1 \end{array} $$
(15)

The search space I for the optimization problem is:

\(I\triangleq \prod _{j=1}^{k}{\left [\alpha _{jmin},\alpha _{jmax}\right ]=\prod _{j=1}^{k}\left [0,1\right ]}\)

Particle swarm optimization (PSO) has the advantages of easy description and understanding, strong search ability and simple programming. Therefore, for the above optimization problem, we choose PSO algorithm for intelligent optimization. Due to the limitation of population diversity, the PSO algorithm appears premature convergence, so we adopt the Modified Particle Swarm Optimization (MPSO) Algorithm which introduces the reverse flight of mutation particles [26]. This algorithm can effectively avoid falling into local optimum in the iterative process.

When solving optimization problems, particles in the swarm \(\left \{X_{i}^{L}\right \}_{i=1}^{N}\) move in search space I to find the best position X, i.e., α. N is the size of the particle swarm and the number of iterations is L. The position and velocity vectors of the ith particle in the evolutionary L generation are expressed as follows:

$$ \left\{ \begin{array}{ll} X_{i}^{L}=&\left[x_{i1}^{L},x_{i2}^{L},\dots,x_{ik+1}^{L}\right]\\ v_{i}^{L}=&\left[v_{i1}^{L},v_{i2}^{L},\dots,v_{ik+1}^{L}\right] \end{array} \right. $$
(16)

where, \(v_{i}^{L}\in M,M\triangleq \prod _{i=1}^{k+1}\left [{-v}_{i\max },v_{i\max }\right ],v_{i\max }=\frac {1}{2}\left (\alpha _{j\max },{-\alpha }_{j\max }\right)\)

This is an optimization problem with constraints. Therefore, the penalty function method is used to deal with the constraints [27], and the fitness function is defined as follows:

$$ {}F(X)= \left\{\begin{array}{ll} f(X)& X\in F\\ f(X)+r\sum\limits_{i=1}^{2k+3}{f_{i}(X)+\varphi\left(X,L\right)}\qquad &X\in I-F \end{array} \right. $$
(17)

Where, r represents the penalty factor, fi(X) denotes the constraint violation measure of the infeasible particles on the jth constraint. Moreover, φ(X,L) denotes additional heuristics value for infeasible particles in the Lth generation of the algorithm[27]. fi(X) expressed by Eq. (19).

$$ {}f_{i}\,=\, \left\{\! \begin{array}{lll} \text{max}\left(0,-X(D)\right), &1\le i\le k+1\\ \text{max}\left(0,X(D)-\frac{U+\sum_{j=1}^{m}N_{j}}{U\ast m}\right),& k+2\le i\le2k+2\\ \left|\sum_{D=1}^{k+1}{X(D)-1}\right|,& i=2k+3 \end{array} \right. $$
(18)

φ(X,L) expressed by Eq. (20).

$$ \varphi\left(X,L\right)=P(L)-\min\limits_{X\in I-F}r\sum_{i=1}^{2k+3}{f_{i}(X)} $$
(19)
$$ P(L)=\max\left(P\left(L-1\right),\min\limits_{X\in F}f(X)\right) $$
(20)

f(X) represents the fitness value of the Lth generation feasible particle. P(L) records the feasible particles with the maximum fitness value obtained by the evolution of the algorithm to the Lth generation. And the value is dynamically updated according to Eq. (21) during the execution of the algorithm. When the algorithm is executed, the update formulas of particle velocity and position are follows as:

$$ {}v_{i}^{L+1}=\omega v_{i}^{L}+c_{1}\text{rand}\left(\right)\left(P_{i}^{L}-X_{i}^{L}\right)+c_{2}\text{rand}\left(\right)\left(g^{L}-X_{i}^{L}\right) $$
(21)
$$ X_{i}^{L+1}=X_{i}^{L}+v_{i}^{L+1} $$
(22)

In the Eq. (22), ω is inertia weight. rand() is a random number evenly distributed in the interval [0,1]; c1 and c2 are two accelerating factors. Defining the individual historical optimal position \(P_{i}^{L}\) of the ith particle is the position with the best fitness value experienced by the ith particle; The global historical optimal location gL is the location with the best adaptive value experienced by all particles in the particle swarm during the evolution.

In addition, the updated formula of inertia weight is as follows:

$$ \omega=\omega_{\min}-\frac{\omega_{\min}-\omega_{\max}}{L_{\max}}L $$
(23)

In order to avoid falling into the local optimal risk, we introduce the reverse of the flight of mutation particles [26], the position and velocity formulas are updated as follows:

$$ v_{i}^{L+1}=-v_{i}^{L} $$
(24)
$$ X_{i}^{L+1}=X_{i}^{L}-v_{i}^{L+1} $$
(25)

The basic parameters of the MPSO algorithm are the population size N is equal to 50, the maximum number of iterations Lmax is 1000, the acceleration factors c1 and c2 are equal to 1.0, and ω[0.4,0.9]; ωmin=0.4; ωmax=0.9.

Results and discussion

Experiment setup

In this experiment, we represent the task arrival node as n1. When njn1, the data transmission rate \(B_{n_{1},n_{j}}\) from node n1 to target node nj is randomly selected from the integer between 80 and 100 Mbps. Otherwise \(B_{n_{1},n_{j}}=\infty \). Data transmission rates \(B_{n_{1},d}\) between edge nodes and cloud nodes are randomly selected between 20 and 30 Mbps integers[28]. The details are shown in Table 1.

Table 1 Simulation parameters

Simulation results and analysis

Effect of number of target nodes on completion time

In this part, we set the total number of normal-load and heavy-load nodes to be 4, the total number of nodes m to be 10, 12, and 14, respectively, and compared the completion time. As shown in Fig. 2, When the task is small, the difference in completion time is not significant. When the task is large, because \(B_{n_{1},n_{j}}=\infty \) when nj=n1, the task assignment to itself will exceed the average task amount of the system, but we limit the size of the subtasks, so the difference of task completion time is significantly increased.

Fig. 2
figure2

The effect of the number of target nodes on the completion time

Impact of system architecture on completion time

Without loss of generality, in the environment of M=12, we analyzed the impact of cloud server on task completion time. The results are shown in Fig. 3,

Fig. 3
figure3

Impact of cloud server on completion time

E-CC denotes the participation of cloud servers, and EC denotes the absence of cloud servers. When there are a few tasks, the impact on task completion time is small. However, when the amount of tasks is large, due to the fast computing speed of cloud computing, the task completion time of the system with cloud servers is obviously better than that of the system without cloud servers.

The effect of total number of nodes on task distribution

In this part, we analyze the distribution of tasks at the edge nodes when the number of nodes is different. And we evaluate the distribution of tasks by load distribution standard deviation (SD)[29], \(SD=\sqrt {\frac {\sum _{j=1}^{m}({\text {Load}}_{n_{j}}-{\text {Load}}_{\text {avg}})_{2}}{m}}\), where \({\text {Load}}_{n_{j}}=N_{j}+u_{j}\), \({\text {Load}}_{\text {avg}}=\frac {\sum _{j=1}^{m}N_{j}+u_{j}}{m}\).

The smaller the standard deviation, the more balanced the task distribution. The result is shown in Fig. 4.

Fig. 4
figure4

The effect of total number of nodes on task distribution

In the case that the heavy-load and normal-load nodes are not assigned new tasks for the time being, the standard deviation of load distribution decreases with the increase of new tasks. That is, with the increase of new tasks, the system gradually tends to a relatively balanced state.

When the new task is small, the more nodes there are, the smaller the average task is, and the more balanced the load distribution is. When the new task is large, due to the number of target nodes is small, it will allocate more tasks and get closer to the average load. Therefore, the more uniform the load distribution, the smaller the load distribution standard deviation.

Comparison of task completion time and load distribution under different strategies

We compare the tasks completion time and the load distribution of our strategy with single node and SDCFN [12]. As shown in Fig. 5.

Fig. 5
figure5

a Effects of different strategies on task completion time. b Effects of different strategies on standard deviation of load distribution

In Fig. 5, n1 denotes that the U is independently completed by node n1, Constraint denotes the results of our load balancing add the \(\alpha _{j}U\leq \frac {\left (U+\sum _{j=1}^{k}N_{j}\right)}{m}\) constraint. Unrestraint denotes the results of our load balancing without constraint. From the Fig. 5a, we can find that the completion time of n1 are larger than our strategy. And due to SDCFN strategy does not consider the completion time of the current tasks of the nodes, the completion time is longer when U<0.97G. When U>0.97G, due to the small number of nodes available for our strategy, its completion time is relatively long. When the task is small, whether to add this constraint has little influence on completion time. When the task is large, because the transmission rate of n1 is , the task it undertakes will be constrained after adding the constraint, so its completion time is longer. From the Fig. 5b, we can find that the load distribution standard deviation of n1 and SDCFN strategy are larger than our strategy. When the task is small, whether to add this constraint has little influence on load distribution standard deviation. When the task is large, the standard deviation of load distribution standard deviation decreases with the increase of tasks after added the constraint. If we do not add this constraint, since the transmission rate of n1 is , the task assigned to itself by n1 will exceed the average load, thus causing the standard deviation of the load distribution of the system to increase.

Conclusion

In this paper, we propose an edge computing network architecture based on the intermediary node. This architecture not only can obtain the state information of the node better, but also can reduce the pressure of edge nodes. On this basis, a task allocation strategy is proposed to balance the load and reduce the task completion time. In this model, the light-load node and the task arrival node are used as the target node to allocate new tasks, while the other nodes are not assigned tasks temporarily, so as to achieve dynamic balancing. Experiments show that this strategy can not only balance the load between nodes, but also reduce the completion time of tasks. When the task is small, our strategy is significantly better than other methods. Finally, we give two alternative strategies. The first is, for tasks with high task completion time requirements, we can adopt the strategy of unconstrained to minimize the completion time. The second is, for the tasks which requirements for completion time are not too high, we can adopt a constrained strategy to better balance the load between nodes and improve quality of service.

Availability of data and materials

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

Abbreviations

COPACA:

Computation offloading, power allocation, and channel assignment

DRL:

Deep reinforcement learning

IoT:

The Internet of Things

IoV:

Internet of Vehicles

MPSO:

Modified particle swarm optimization algorithm

PSO:

Particle swarm optimization algorithm

RSUs:

Road side units

SDCFN:

Software-defined cloud/fog network

SDN:

Software-defined network

TMS:

Traffic management server

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Author information

YY, XS, and QL are the principal contributors in terms of simulation modelling, writing, and the generation/interpretation of numerical results. In a supervising role, GL, JW, and XL formulated the research problem and contributed to the simulation modelling and the discussion of results. All authors read and approved the final manuscript.

Correspondence to Junhua Wu.

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Li, G., Yao, Y., Wu, J. et al. A new load balancing strategy by task allocation in edge computing based on intermediary nodes. J Wireless Com Network 2020, 3 (2020). https://doi.org/10.1186/s13638-019-1624-9

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Keywords

  • Edge computing
  • Load balancing
  • Task allocation
  • State assessment