A QoS-Guaranteed and Congestion-Controlled SDN Routing Strategy for Smart Grid

Abstract

The smart grid (SG) is an integration of a traditional power grid with advanced information and communication infrastructure for a large number of electrical applications. Despite all these advantages that the SG will bring, certain issues arise when designing a high-quality SG communication network. One of the critical challenges is that the existing routing strategies in smart power grids are incapable of guaranteeing differentiated QoS requirements considering the network dynamics. To address this limitation, we propose an SDN routing algorithm called the QoS-guaranteed and congestion-controlled OpenFlow routing strategy (QCORS) to satisfy the various communication demands by utilizing the flexibility of SDN. Gaining from its open and programmable idea in SDN, the proposed strategy is expected to divide the link into different congestion levels based on predicting the future congestion status from transmission links. Then packets are expected to be transmitted to routers through links under lower load conditions. The simulation results have demonstrated that the proposed method can reduce the average peer-to-peer delay of all the vocational flow and guarantee the reliability of the network.

1. Introduction

The growing consumption of electricity attracts more attention to power quality, environmental protection, and cost. Instead, the traditional power grid model [1] has low efficiency and many unsafe factors, making it difficult to meet the increasing demand for electricity. Thus smart grid [2] (SG) is proposed to improve the situation. SGs [2], as electricity supply networks, bring new solutions to optimize the operations of all functional units from electricity generation to end-customers through communication technologies. By introducting the communication system layer to control, monitor, and automate the entire network of power systems [3,4], the SG becomes more flexible. The hierarchy of the SG is shown in Figure 1. Nowadays, with the implementation of many recent network technologies [5,6,7,8,9], the power grid has new requirements on availability and reliability.

As shown in Figure 1, there are many applications in the power system layer (a), including power production units, power transmission networks, power distribution networks, etc. Communication serves as the backbone in the creation of all the involved applications and technologies. According to characteristics of diverse applications, the smart grid applies different communication technologies in the communication layer (b) to make the power system intelligent. Specifically, the SG supports different applications based on the integrated high-speed two-way communication network, such as advanced measurement system, demand response (DR) [10], and distribution automation (DA) [11]. Moreover, the data communication network associated with the power grid consists of three parts: the wide area network (WAN), the neighborhood area network (NAN), and the home area network (HAN). As the “last kilometer” of data collection and user access in the SG, NAN needs to provide high quality of service (QoS) for different power application services in particular.

Although many approaches have been proposed to achieve high QoS in NAN, its personalized QoS requirements for diverse applications [12] are difficult to meet. For example, video monitoring, as a general service in daily life, is expected to balance including delay and packet loss rate [13]. Instead, for some other applications, their QoS requirements are to keep stable data transmission rates. Hence, there are great challenges to the SG NANs neighborhood area network because of the diverse heterogeneous applications and distinguished QoS requirements. There is an urgent demand for a controllable, flexible, and open business platform to realize a unified controlling and coordinated scheduling of the SG [14]. Moreover, it is critical to find a unified solution for the SG to improve the utilization and QoS simultaneously under a time-varying network. In this paper, we associate the QoS demand with the congestion control [15,16,17] to transform such a hard-evaluated metric into a more realistic one.

A software defined network (SDN) [18,19,20] presents a solution by separating the function of the network controlling from data transmission and brings several advantages. On the one hand, the controlling plane is capable of optimizing networks by management to transfer all complex computational tasks (including QoS analysis and decisions) from hardware to a centralized control [21,22]. On the other hand, the overall network latency has been improved and the data plane only focuses on the data processing [23,24]. Thus, SDN is widely used as an improvement to the SG because of its flexibility. To further verify the feasibility of SDN in the power communication network, a research team [25] found that the centralized controllers of SDN can integrate the resources of the SG dynamically to make the network on-demand, flexible, and robust [26].

The flexible open interfaces in SDN can either realize the on-demand call for different services or handle the process of controlling by programming. The application of SDN in SG is described in Figure 2.

Due to the strong heterogeneity [27] in services and large difference in QoS requirements for SG NAN, the way to provide solutions for each kind of service to meet the link utilization and QoS requirements under the time-varying network resources has become one of the key issues of SG. By utilizing the advantages of SDN controllers, we design a neighbor-routing mechanism, which can balance the neighbor traffic with different service requirements in real time automatically. By considering the data size and the traffic flow, our method is capable of not only monitoring the congestion level of each node in the network, but  also meeting the low delay requirement for distinguished applications. In addition, our apporach increases the flexibility and reliability of the SG communication networks. In summary, our main contributions can be summarized as follows.

• To meet the QoS requirements of different service flows in the SG, by focusing on the flow trends in the network, we design an SDN-based strategy to predict the future congestion status for the link and construct a virtual congestion-free topology.
• We propose a queueing model and construct a long-term network utility maximization problem, which can be effectively solved by the Lyapunov optimization theory, to determine the final routing decision.
• The experimental results of different algorithms show that our QCORS can effectively grasp the advantages of global network and reduce end-to-end delay and packet loss rate.

The rest of this article is organized as follows. Section 2 introduces the research background and Section 3 describes the concrete implementation process of the QCORS mechanism. In Section 4, the performance of the QCORS mechanism is verified by constructing an experimental platform. Section 5 presents a summary of the paper.

2. Related Works

With the combination of SG and new energy, research on various aspects of the power grid are increasing. Based on the high-dimensional random matrix theory, Zhang et al. [28], analyzed the spectral distribution of eigenvalues of the high-dimensional random matrix covariance matrix for massive power consumption data. Based on the statistical characteristics of the random matrix, a method of power status recognition based on the big data of power consumption is proposed. Although this method can meet the requirements of visualization, timeliness, reliability, and security of the power grid, it focuses on the power consumption of the grid and does not consider the service quality requirements of different business flows in the SG, and the communication quality is not guaranteed. SG communication networks must support a variety of different QoS requirements of the application. The current network infrastructure cannot dynamically adapt to the requirements of various applications in the SG [29]. In order to solve this problem, Kim et al. [30] presented an SDN application in the SG, and designed a system architecture for the SG environment. For those SG frameworks supporting SDN, they are beneficial to process flows in micro size. Sydney et al. [31] proposed a mechanism, by deploying OpenFlow technology on SG, to provide automatic fault recovering, load balancing, and QoS guarantee. The algorithm creates two virtual network interfaces to isolate high-priority data streams and best-effort data streams. The data rate of the virtual interface is dynamically configured according to the queue size and can control traffic in the network.

For the SDN network, based on the characteristics of the global management of the controller in the OpenFlow network, it can not only meet the requirements of different QoS, but also can better monitor the resources of the network. At present, the research on the congestion management mechanism under the OpenFlow network framework has had some achievements. Handigol et al. designed a LOBUS algorithm for the SDN network, which simply applies the greedy selection strategy to select the path with the least response time [32]. However, this solution that attempts to use a comprehensive load-balancing algorithm ignores the unpredictable changes in load state, and when the network grows more and more, the network conditions are less controllable. On this basis, Long et al. in [33] introduced a new dynamic balance flow-routing algorithm, namely LABERIO, to monitor the distribution of traffic in the network. LABERIO sets a congestion threshold, which finds the most congested links in the network according to thresholds. Then, it finds the data stream which occupies the maximum bandwidth of the link to redirect routing. Although the LABERIO algorithm prevents the occurrence of network congestion with a certain probability, it only considers the data flow bandwidth parameters, ignoring the requirements of other business attributes. Thus, the network sensitivity and accuracy can not be guaranteed. Nguyen et al. proposed an algorithm, OFFICER, for the path allocation linear optimization model, which creates a default route for all communications [34]. After that, it introduces some deviations from this path and utilizes those deviations to arrive at the destination through different strategies. However, refs. [35,36], when the data in the network is higher, the table items in the flow table will also increase correspondingly, and the use of this algorithm can reduce the service quality of the packets. However, existing approaches have ignored either the dynamic changes of congestion or personalized QoS demands. In addition, the existing solution for such optimization problem is not optimal. Thus, focusing on diverse QoS requirements, we propose QCORS to construct the uncongested routing topology dynamically and adopt the Lyapunov theory to solve the optimization problems.

3. Design of QCORS Algorithm

In this section, we will elaborate on the proposed QCORS in detail. Generally, before the link congestion actually occurs, the traffic on the overloaded link should be transferred to the remaining free links to meet the different QoS requirements of the SG application and improve the link utilization. Based on this idea, QCORS predicts the link loads by analyzing the overall network status and then constructs the virtual uncongested topology. To make final routing decisions, a queueing model is first constructed and further solved by the Lyapunov optimization theory [37,38]. The dynamic analysis of the congestion state not only helps solve the congestion problem of the network, but also guarantees the reliability of the application [39]. By QCORS, the whole network could be continuously re-scheduled according to the application priorities. A list of acronyms used throughout the paper is presented in

Table 1. The abbreviations and the corresponding definitions.

Abbreviations	Definitions
AMI	Advanced Metering Infrastructure
DR	Demand Response
DA	Distribution Automation
HAN	Home Area Network
LABERIO [33]	LoAd-BalancEd Routing wIth OpenFlow
LOBUS [32]	LOad-Balancing over UnStructured networks
NAN	Neighborhood Area Network
QoS	Quality of Service
QCORS (our work)	QoS-guaranteed and Congestion-controlled OpenFlow Routing Strategy
SG	Smart Grid
WAN	Wide Area Network

.

3.1. Sdn System Framework

SDN is an open and programmable [40,41] architecture, which can obtain the global topological structure of the whole network. It is flexible and controllable, with strong real-time performance and good robustness. The central idea of SDN [42] is to decouple the traditional network architecture that is closely connected with the network equipment at all levels, and obtain a completely disconnected data layer and control layer. Based on this, standardization is implemented at all levels to realize centralized management and control. The established SDN system consists of three parts: the application layer, the control layer, and the forwarding layer.

Specifically, the forwarding layer includes some basic network equipments, which does not have the control ability. Its main target is to complete the data forwarding and processing according to the command of the control layer [43]. The application layer of SDN involves the application of various businesses. In particular, the application layer communicates with the control layer through the northbound interface, where the northbound interface is an upward interface provided to operators or users for access and management. The application layer is composed of various software written by users. The user can thus invoke the API provided by the controller according to his own needs to innovate the network service. The SDN controller creates a logically centralized plane, which provides global control over all SDN node-based physical topologies connected to the controller, making fine-grained control of SG services possible. The control layer is the core part of the whole network, including network link discovery, topology management, network routing strategy, etc. SDN conducts centralized management and control over the whole network through the control layer. The southward interface is a downward provided interface, and the control layer and the data forwarding layer communicate and interact with each other through this interface. Currently, the mature southward interface protocol is OpenFlow protocol.

Due to SDN having coordinated the different types of devices and different communication protocols for data-forwarding layers by standardization, the devices are expected to receive instructions from the control layer. Then, the message can be smoothly transmitted according to the forwarding demand. This design pattern can support different types of traffic flows and develop an optimized routing algorithm.

3.2. Network Model

In this section, we present our network model and the optimization framework in combination with the current SG architecture. To better utilize the Lyapunov optimization [38,44] in our framework, we transform delay into queue length to simplify the analysis. Suppose that the SDN controller has optimized the network k times in the duration T, then the T is divided into k time slots. Each slot is denoted as t.

Given a communication network model, the network topology is defined as a undirected graph composed of communication links and nodes, such as $G=\{N,L\}$. Among them, $N=\{n_1,\cdots ,n_i,\cdots ,n_m\}$ represents the set of switches or terminals in the network, where m is the total number of nodes. In addition, L represents the set of physical links. Given the source node and destination node $n_s$ and $n_d$ respectively. The packet transmission path $P_{sd}^t$ (suppose $n_s$ and $n_d$ are not directly connected) at time t consist of a series of node pairs, such as $P_{sd}^t=\{(n_s,n_{s1}),\cdots ,(n_j,n_i),(n_i,n_k),\cdots ,(n_{d1},n_d)\}$. It is noted that every element in $P_{sd}^t$ is physically connected. For the target node $n_i$, $I\left(n_i^t\right)=\{n_s,\cdots ,n_j\}$ represents the set of predecessors whereas $O\left(n_i^t\right)=\{n_k,\cdots ,n_d\}$ represent the set of successors.

3.3. Link Congestion Degree Judgment

The algorithm proposed in this paper uses OpenFlow to detect the status of the network. When an application is activated suddenly in SG, it may introduce huge quantities of emergency messages in certain links [45,46], thus resulting in transient congestion. Then, QCORS will make decisions on whether the packets need to be processed by sensing the condition of congestion from the link.

Definition 1.

Link load $C\left(P_{sd}^t\right)$. For a given network topology, the SDN controller is expected to regulate the entire network based on the network load dynamically. Then time slot t, the packet transmission path $P_{sd}^t$ consist of a series of node pairs $\{(n_s,n_{s1}),\cdots ,(n_j,n_i)$,$(n_i,n_k),\cdots ,$$(n_{d1},n_d)\}$. To simplify, we denote $(n_i,n_j)$ as $p_{ij}$. Then, the average transmission rate between the $n_j$ and $n_i$ is $v\left(p_{ij}\right)$. Thus, for the time duration t, the overall link load $C\left(P_{sd}^t\right)$ equals the average transmission rates $\left\{v\left(p_{ij}\right)\right|p_{ij}\in P_{sd}^t\}$ divided by the bandwidth of the link:

$$C\left(P_{sd}^t\right)=\frac{{\sum }_{p_{ij}\in P_{sd}^t}v\left(p_{ij}\right)}{B_{sd}},$$

(1)

where $p_{ij}$ denotes the physical link between node $n_i$ and $n_j$. The flow rate of each data stream is $\left(v_1,\cdots ,v_k,\cdots ,v_n\right)$ respectively, and $B_{sd}$ indicates the bandwidth of link $P_{sd}$.

The SDN controller can master the global topology of the entire network and evaluate the degree of congestion in the network by periodic monitoring of the network. In Equation (1), the sum of all the data flows in link $P_{sd}$ occupying the bandwidth of the link can reflect the load of the different links in the network well. The more data streams, the higher the link load.

However, in traditional methods, the route is expected to be switched once the link load is identified as large [47,48]. This brings a negative effect on the network stability. Thus, how to reduce the frequency of route switching is also critical. In this paper, the exponentially weighted moving average (EWMA) algorithm is introduced here to calculate the rectified link load. The controller periodically monitors the status of the link every $\mathrm{\Omega }$ seconds and calculates the rectified link load in successive cycles as follows:

$$\overline{C\left(P_{sd}^t\right)}=(1-\alpha )C\left(P_{sd}^t\right)-\alpha C\left(P_{sd}^{(t-1)}\right),$$

(2)

where $\alpha$ is transition probability of congestion which ranged between 0 and 1. Generally, $\alpha$ is set to 0.1 or 0.01 [24], and we set $\alpha$ to 0.1 in this paper. By introducing Equation (1),  Equation (2) can be rewritten as:

$$\overline{C\left(P_{sd}^t\right)}=\frac{(1-\alpha ){\displaystyle \sum _{p_{ij}\in P_{sd}^t}}v\left(p_{ij}\right)+\alpha {\displaystyle \sum _{p_{ij}\in P_{sd}^{(t-1)}}}v\left(p_{ij}\right)}{B_{sd}}.$$

(3)

Then, we could calculate the congestion level according to

Table 2. Link load and congestion level mapping.

Value of Congestion Level	Traffic Load Range at Link $\mathbf{sd}$
(1) No congestion	$\overline{C\left(P_{sd}^t\right)}\le C{\left(P_{sd}^t\right)}_{low}$
(2) Low congestion	$C{\left(P_{sd}^t\right)}_{low}\le \overline{C\left(P_{sd}^t\right)}\le C{\left(P_{sd}^t\right)}_{high}$
(3) Heavy congestion	$\overline{C\left(P_{sd}^t\right)}\ge C{\left(P_{sd}^t\right)}_{high}$

, where the $C{\left(P_{sd}\right)}_{low}$ and $C{\left(P_{sd}\right)}_{high}$ are identified through the empirical analysis.

3.4. Packet-Redirection Strategy Model

For a given topological pattern, the paths between nodes are calculated by the controller based on the routing algorithm. Routes between a pair of nodes are generally not recalculated unless the topology changes [49]. In this case, when an application flow breaks out, some key links may carry excessive loads. In the previous section, because the link load has been mapped to different levels of congestion, the controller can deal with the links according to the detected situation. Let $G^{\prime }$ denotes a new virtual topology called no congestion link. In this case, if there is a link that is determined to be congested. It is supposed to be blocked to achieve a better transmission performance. An example is shown in Figure 3. Suppose the left one is the original communication topology, and the center link is considered a congested link. Then for the next coming packet, it will choose other links rather than the congested one even if it has to go through more hops to the destination.

(1) Data collection: The node collects data from its predecessor and sends it to the successor. The range of data collection for node n is:

$$0\le \sum _{a\in I\left(n^t\right)}{x}_n^t\left(a\right)\le x_{max},\forall n\in N,$$

(4)

where $x_n^t\left(a\right)$ denotes the amount of data collected by node a in slot t. In addition, $a\in I\left(n^t\right)$ represents the set of all predecessor nodes of node n at time t, and $x_{max}$ indicates the maximum data size collected by any node in the time slot.

(2) The amount of transmission of the node. Considering time-varying characteristics of link capacity, it is assumed that link capacity is independent and identically distributed in different time slots. Moreover, all the output data should be less than or equal to the link capacity. Thus the transmitted data amounts of node n should have the following constraints:

$$0\le \sum _f\sum _{b\in O\left(n^t\right)}{x}_n^t(b,f)\le C_n^t\left(b\right),\forall b\in O\left(n\right),$$

(5)

where $C_n^t\left(b\right)$ represents the link capacity of the link $(n,b)$. Let $x_n^t(b,f)$ denote the sum of f class data transferred between nodes $(n,b)$ in slot t. In addition, in slot t, the amount of data that node n sends to node b cannot exceed $Q_n\left(t\right)$, which is the total queue size in node n at current time t:

$$0\le \sum _{b\in O\left(n^t\right)}{x}_n^t\left(b\right)\le Q_n\left(t\right),\forall n\in N.$$

(6)

Based on Lyapunov optimization [37,38,44], the network can guarantee stability only if the following inequality can be satisfied,

$$\underset{T\to \infty }{lim}\frac{1}{T}\sum _{t=0}^{T-1}\sum _{n\in N}E\left[Q_n\left(t\right)\right]<\infty ,$$

(7)

where $Q_n\left(t\right)$ denotes the length of the data queue at node n in slot t. This means the total queue length in the system is bounded in the case of an infinite horizon.

(3) Data queue model: $Q_n^f\left(t\right)$ then represents the queue occupied by data of class f. The dynamic of $Q_n^f\left(t\right)$ in slot t is

$$Q_n^f\left(t+1\right)=Q_n^f\left(t\right)+\sum _{a\in I\left(n\right)}{x}_n^t(a,f)-\sum _{b\in O\left(n\right)}{x}_n^t(b,f).$$

(8)

(4) Problem model: Our optimization goal is to maximize the average network utility under the constraints of the entire network. The utility function $U\left(t\right)$$U_f\left(t\right)$ uses the logarithm function i.e., $U\left(t\right)=log(1+{\displaystyle \sum _{a\in I\left(n\right)}}{x}_n^t\left(a\right))$, which is a limited concave function that has continuous and non-decreasing second derivative. Then the optimization problem can be given by

$$\begin{array}{cc}\hfill max& \overline{O\left(t\right)}=\underset{T\to \infty }{lim}\frac{1}{T}\sum _{t=0}^{T-1}E\left\{U\right(t\left)\right\}\hfill \\ \hfill s.t.& 0⩽\sum _{a\in I\left(n\right)}{x}_n^t\left(a\right)⩽x_{max},\forall n\in N,\hfill \\ \hfill & 0⩽\sum _f{x}_n^t(b,f)⩽C_n^t\left(b\right),\forall b\in O\left(n\right),\hfill \\ \hfill & 0⩽\sum _{b\in O\left(n\right)}{x}_n^t\left(b\right)⩽Q_n\left(t\right),\forall n\in N,\hfill \\ \hfill & \underset{T\to \infty }{lim}\frac{1}{T}\sum _{t=0}^{T-1}\sum _{n\in N}E\left[Q_n\left(t\right)\right]<\infty .\hfill \end{array}$$

(9)

Because the optimization problem includes a dynamic queue model, it is difficult to be solved by existing convex optimization tools. In this paper, we use the Lyapunov optimization theory, which is generally used to deal with the dynamic problem.

(5) Lyapunov optimization algorithm: Although the Lyapunov function has many kinds of expressions, the second method of the Lyapunov function [50] is most widely used, which is defined as follows:

$$L\left(Q\left(t\right)\right)=\frac{1}{2}\sum _n\sum _f{Q}_n^f{\left(t\right)}^2.$$

(10)

Then, we define the Lyapunov Drift by $\Delta \left(t\right)$. This represents the expected value of change for the Lyapunov function from slot t to slot $t+1$. Thus, the Lyapunov drift for a single slot is defined as

$$\Delta \left(t\right)=E\left\{L\left(Q\right(t+1\left)\right)-L\left(Q\right(t\left)\right)\mid Q\left(t\right)\right\},$$

(11)

where $\Delta \left(t\right)$ represents the trend of $L\left(Q\left(t\right)\right)$ over one time slot. Moreover, for a specific slot t, the smaller $\Delta \left(t\right)$ means slower growth rate of $L\left\{Q\left(t\right)\right\}$. By minimizing the Lyapunov shift $\Delta \left(t\right)$ in each time slot, the stabilized data queue that satisfied the delay constraint can be achieved. The network utility function can be integrated into the Lyapunov drift $\Delta \left(t\right)$ to further obtain the drift-minus-utility [51] function $\Delta V\left(t\right)$:

$$\Delta V\left(t\right)=\Delta \left(t\right)-VE\left[O\left(t\right)\left|Q\left(t\right)\right.\right],$$

(12)

where V is a nonnegative weight, which represents the network utility $O\left(t\right)$ in the proportion of $\Delta V\left(t\right)$. The higher value of V, the higher proportion of $O\left(t\right)$ in $\Delta V\left(t\right)$ [34]. By minimizing $\Delta V\left(t\right)$, the queue length in SDN network can be stabilized, and the network throughput is also improved.

Lemma 1.

If there is a constant $B\ge 0$, $V\ge 0$, $\xi \ge 0$, in all time slots t = 0, 1, 2, ... and the possibility of all queue $Q\left(t\right)$, the upper bound of $\Delta V\left(t\right)$ is

$$\Delta \left(t\right)-VE\left[O\left(t\right)\left|Q\right(t)\right]⩽B+E\left[\tilde{\Delta }u\left(t\right)|Q\left(t\right)\right].$$

(13)

Proof of Lemma 1.

Because $Q\ge 0$, $b\ge 0$, $A\ge 0$, $\left[{\left(Q-b\right)}^{+}+A^2\right]⩽Q^2+A^2+b^2+2Q\left(A-b\right)$, then

$$\begin{array}{c}L\left\{Q\right(t+1\left)\right\}-L\left\{Q\right(t\left)\right\}\hfill \\ =\frac{1}{2}{\displaystyle \sum _n}{\displaystyle \sum _f}\left[Q_n^f{(t+1)}^2-Q_n^f{\left(t\right)}^2\right]\hfill \\ =\frac{1}{2}{\displaystyle \sum _n}{\displaystyle \sum _f}\left\{\begin{array}{c}{\left({\left(Q_n^f\left(t\right)-{\displaystyle \sum _{b\in O\left(n\right)}}{x}_n(b,f)\right)}^{+}+{\displaystyle \sum _{a\in I\left(n\right)}}{x}_n(a,f)\right)}^2\hfill \\ -Q_n^f{\left(t\right)}^2\hfill \end{array}\right\}\hfill \\ ⩽\frac{1}{2}{\displaystyle \sum _n}{\displaystyle \sum _f}\left[\begin{array}{c}{\left({\displaystyle \sum _{a\in I\left(n\right)}}{x}_n(a,f)\right)}^2+{\left({\displaystyle \sum _{b\in O\left(n\right)}}{x}_n(b,f)\right)}^2+\\ 2Q_n^f\left(t\right)\left({\displaystyle \sum _{a\in I\left(n\right)}}{x}_n(a,f)-{\displaystyle \sum _{b\in O\left(n\right)}}{x}_n(b,f)\right)\end{array}\right].\hfill \end{array}$$

(14)

   □

Note that B can be seen as a constant in practical problems, which satisfies

$$B⩾\frac{N^2}{2}\left(x_{max}^2+C_{max}^2\right).$$

(15)

Then $\tilde{\Delta }u\left(t\right)$ can be given as follows:

$$\tilde{\Delta }u\left(t\right)=\sum _n\sum _f\left[\begin{array}{c}{Q}_n^f\left(t\right)\left({\displaystyle \sum _{a\in I\left(n\right)}}{x}_n(a,f)-{\displaystyle \sum _{b\in O\left(n\right)}}{x}_n(b,f)\right)-VU\left(t\right)\hfill \end{array}\right].$$

(16)

According to Lyapunov drift theory [52], the maximum time-averaged network utility problem can be transformed into a minimized drift function problem. This can be done by removing the queue stability constraint and turning a time-averaged problem into a dynamic programming problem, which makes the optimization problem (9) further simplified as the following optimization problem (17):

$$\begin{array}{cc}\hfill min& \tilde{\Delta }u\left(t\right)\hfill \\ \hfill s.t.& 0⩽\sum _{a\in I\left(n\right)}{x}_n^t\left(a\right)⩽x_{max},\forall n\in N\hfill \\ \hfill & 0⩽\sum _f{x}_n^t(b,f)⩽C_n^t\left(b\right),\forall b\in O\left(n\right)\hfill \\ \hfill & 0⩽\sum _{b\in O\left(n\right)}{x}_n^t\left(b\right)⩽Q_n\left(t\right),\forall n\in N.\hfill \\ \hfill \end{array}$$

(17)

In each slot t, all the states in the network can be seen as known quantities. This article only studies the routing in the network, and we can simplify the problem as follows:

$$\begin{array}{cc}\hfill min& Q_n\left(t\right)-x_n^t(b,f)-VU\left(t\right)\hfill \\ \hfill s.t.& 0⩽x_n^t(b,f)⩽C_n^t\left(b\right),\forall b\in O\left(n\right)\hfill \\ \hfill & 0⩽x_n^t(b,f)⩽Q_n\left(t\right),\forall n\in N\hfill \\ \hfill & 0⩽Q_n\left(t\right)⩽Q_{max},\hfill \end{array}$$

(18)

where $Q_{max}$ represents the maximum queue length of the node. Because the utility function $U\left(t\right)$ is a concave and derivative function, the throughput issue is a convex optimization problem. Let $U^{*}\left(t\right)$ be the optimal solution of this problem, based on convex optimization theory [53], and the $U^{*}\left(t\right)$ is achieved by

$$U^{*}\left(t\right)={[U^{{}^{\prime }-1}(\frac{Q_n^f\left(t\right)}{V})]}_0^{Q_{max}},$$

(19)

where $U^{{}^{\prime }-1}(.)$ represents the first derivative of the inverse function of the utility function $U(.)$ and ${\left[x\right]}_a^b=min(max(x,a),b)$. The process of QCOSR is illustrated in the Algorithm 1.

Algorithm 1 QCORS

Input: Input the Network topology G, initialize the parameters of differentiating packets and their priority, set the congestion level threshold value $C{\left(P_{sd}\right)}_{low}$, $C{\left(P_{sd}\right)}_{high}$, and V. Output: Output the path from s to d with optimal routing. 1: Calculate the link congestion $\overline{C\left(P_{sd}^t\right)}$ between node s and node d 2: while$\overline{C\left(P_{sd}^t\right)}\ge C{\left(P_{sd}\right)}_{low}$do 3:     Check a new topology $G^{\prime }$ 4:     Obtain the current optimal path based on the Equation (18) 5:     if $C{\left(P_{sd}\right)}_{low}⩽\overline{C\left(P_{sd}^t\right)}⩽C{\left(P_{sd}\right)}_{high}$ then 6:         Select the packet with the highest priority for the new route 7:     end if 8:     if $\overline{C\left(P_{sd}^t\right)}⩾C{\left(P_{sd}\right)}_{high}$ then 9:         Select a new routing transmission except for video packets 10:     end if 11: end while

4. Experiments and Performance Analysis

4.1. Implementation Details

In this section, the proposed algorithm is implemented by using the floodlight controller [54] in the experimental environment of Linux Ubuntu14.04. In the floodlight controller, we mainly add two modules. One is used to detect link congestion periodically, and another one is to find the optimal route according to the optimization function. The controller adds the code of the QCORS algorithm and recompiles the simulation software. The experiment topology was built by using Mininet 2.0.0, and the southbound interface protocol used Openflow 1.3. SDN network topologies of 2 to 36 nodes are used to simulate the network of smart power grid neighbors, and the link bandwidth is 100 M, and the maximum length of each queue is 1000 packets. The simulation time is 600 s, and the average value of each experiment is repeated 10 times. The value of V (defined in Equation (12)) is 1000. An example of SDN network simulation with 10 nodes in our experiments is shown in Figure 4. Moreover, some NAN applications are configured and differentiated as shown in Table 2. It is noted that those applications have all been activated in the simulation simultaneously. In other words, though the congestion level varies over time, the network is always congested.

4.2. Performance on Different Applications

In this section, we compare the performance of the proposed strategy on different applications, wherein the basic setting is shown in Section 4.1. It is noted that, for an arbitrary node, it will randomly select another node to perform one of the designed applications from the table. Therefore, to reduce the bias caused by such randomness and make the experimental results more accurate and robust, we have conducted experiments on each kind of topology ten times and adopted the average value as the final result.

Figure 5a shows the end-to-end delay comparison of data packets for different service flows (AMI/power management, requested AMI/power quality, periodic AMI/power quality, video surveillance). From Figure 5a, as the network node number increases, the network load also increases. At this point, the time of packet staying in the queue also increases. The QCORS considers the extent of the congestion in the middle forwarding link, and leads the packet to the lighter path according to the link load. Thus, the proposed algorithm reduces the queuing time of the packet, and leads to different end-to-end delays of different priorities. It can also guarantee the delay and reliability of the higher-priority data, and reduce the congestion degree of the network.

Figure 5b shows the variation of the average packet loss rate of four different priorities in the neighborhood network. It can be seen from the figure that in the case of fewer network nodes, the mechanism can guarantee the QoS requirement of different service flows. When the network congestion is aggravated, the QCORS mechanism guarantees QoS of packets by prioritizing the higher-priority packets. Therefore, the higher priority, the smaller packet loss rate.

4.3. Performance Comparison with Baselines

In this section, we compare the performance of LOBUS, LABERIO, OFFICER, and QCORS on different network topologies. The comparison on those approaches are shown below.

• LOBUS [32]: This method directly use the greedy selection strategy to select the path with the least response time, and instead ignores the unpredictable changes in the load state.
• LABERIO [33]: Although LABERIO monitors the distribution of traffic in the network, it only considers the data flow bandwidth while ignoring the requirements of other business attributes.
• OFFICER [34]: This approach introduce some additional deviations to the path allocation and utilizes those deviations to arrive at the destination through different strategies. However, the increasing data reduce the service quality of this method.

To address this limitation, our proposed SDN routing algorithm, QCORS, is expected to divide the link into different congestion levels based on predicting future congestion status from transmission links. Then packets are expected to be transmitted to routers through links under lower load conditions.

Figure 6a shows the comparison of the average end-to-end delay of the network with the network size of the four routing mechanisms. When the network is congested, the QCORS is overloaded by the intermediate link load-aware congestion criteria and provides a lighter link for different traffic flows according to the priority. The QCORS algorithm implements congestion control in the network and reduces routing concussion and the congestion of the network. From Figure 6a, we can see that LOBUS is a global load algorithm. When the network is growing, its delay is uncontrollable. LABERIO does not optimize the routing criteria for different service QoS requirements. Although the OFFICER algorithm considered this issue, the processing delay of the different strategies is costly, so the time delay of the LABERIO algorithm and OFFICER algorithm is not much different.

The average packet delivery rate of the four routing strategies varies with the size of the network as shown in Figure 6b. The network load is lighter when the number of nodes is less than or equal to 16. In addition to the LOBUS, the average packet loss rates of the other three strategies are below 10%. The packet delivery rate of LOBUS algorithm decreases rapidly due to the defect of the routing criterion and routing mechanism, whereas the other three routing mechanisms improve the reliability of the whole network through a multi-route optimization strategy. Although LABERIO also considers the possibility of congestion in the network, it does not take QoS requirements for different application flows into account. The OFFICER mechanism guarantees a certain QoS requirement, but cannot provide distinguish service for different priorities. The QCORS algorithm proposed in this paper not only considers the packet transmission rate, but also takes the length of the network node cache queue into account. Therefore, QCORS has the lowest packet loss rate.

Figure 6c clearly shows the jitter of the four algorithms. The link jitter reflects the stability of the whole network, and performs as an important indicator of the communication service quality. When the link jitter is large, the quality of the whole communication network will decline rapidly, and it cannot provide good service to users. It can be seen from the results that the link jitter of the four algorithms increases with the increase of the number of nodes, but overall, QCORS performs best, whereas the LOBUS algorithm is the most unstable and performs the worst. As can be seen from the end-to-end delay results in Figure 6a, QCORS performs well. Because QCORS is designed to reduce end-to-end latency, the algorithm also helps reduce jitter and optimizes link stability.

4.4. Limitations

Although our method effectively controls the network congestion and improves the QoS, it still has several limitations. First, in our designed approach, many parameters are assumed artificially. Instead, at present, deep learning has been widely used in many different fields, and has achieved remarkable results. Thus, we will use deep learning technology to optimize the relevant parameters in the SDN routing strategies in our future works. Secondly, due to the more complex network and more diverse types of data and equipment resources, it brings more serious security threats. How to build a secure and privacy-persevering mechanism for the SDN routing protocol in SGs is the next step to be considered.

5. Conclusions

Based on the QoS requirements of different application streams in SG neighbor regional networks, this paper presents a QoS-guaranteed and congestion-controlled SDN routing method. First, the congestion levels of link loads in the network are analyzed. According to the analysis results, congestion mapping can find the congestion link in a continuous period, and the congestion link is processed by building a virtual non-congested topology to replace the congested link. Secondly, an optimal frame is introduced into the system for the purpose of maximizing the utility of the whole network considering the new virtual topology. We propose a dispatching algorithm for the nodes in the network guiding packets to select the appropriate route, according to the various needs of SG packets. Numerical results illustrate that the QCORS method proposed in this paper is better than many existing methods in terms of end-to-end delay and packet losing rate. Therefore, the method of this paper is feasible and efficient.