Wireless Software Defined Network (WSDN) presents a new network architecture where the control plane of forwarding devices is shifted to a centralized controller. It is critical to maximize network throughput and keep the network stable during congestion control. However, stability control is insufficient to achieve these aims in the presence of delay and interference. In this paper, we adopt robust control to tackle these problems. Firstly, an efficient weighted scheduling scheme is proposed to maximize the network throughput. Secondly, a robust control model is presented, which is analyzed by Lyapunov-Krasovskii functionals. The sufficient conditions are formulated by Linear Matrix Inequalities (LMIs). Finally, a numerical simulation is conducted to indicate the effectiveness of the proposed scheme.

In Wireless Software Defined Networks (WSDNs), the control plane of the forwarding devices is shifted to a centralized controller [

Some existing solutions would prefer to analyze a robust control for network congestion in SDNs [

In general, the current researches have three crucial limitations. Firstly, the control policies are not located in the centralized controller but implemented by flow tables in the forwarding devices. Secondly, propagation delay is seldom considered in device-controller pairs during congestion control. Finally, the traditional theories for robust control do not work well in WSDNs.

In this paper, to obtain the robust control with the maximal global throughput in WSDNs, a new robust control model is proposed by using Lyapunov-Krasovskii functionals [

Our main contributions in this paper are listed as follows:

Presenting a realistic global control strategy and the analysis scheme of delay and interference in WSDNs: scheduling scheme currently implemented in the centralized controller can achieve stability control through the global view of real WSDN with the external interference; additionally, the propagation time-delay is essential in real WSDNs and we define an upper bound of delay as the network propagation delay and analyze its influences in global view of WSDN.

Proposing a general and effective approach to the global robust congestion problem, by calculating optimized values for network parameters with a weighted fair scheduling scheme, and maintaining that optimized status via transformation of a closed-loop network model to a normal robust

An interdisciplinary effort is made to construct a robust control strategy by combining the stability analysis theories and congestion control principles of wireless network. Taking advantages of the applicability of Lyapunov-Krasovskii functionals in stability analysis of WSDN, the paper achieves the desired global robust control for network congestion.

The rest of the paper is organized as follows. Section

In the recent years, congestion control in WSDNs has attracted considerable attention. Numerous researches have offered stability and robust control algorithms for congestion control in many wireless network scenarios, for example, WSN and VANET, to achieve robust control for network congestion.

Stability control of network congestion has drawn widespread attention and research interests [

Robust control has attracted particular interest in the literature for the traditional network control system. Based on the wireless characteristic, robust congestion for network congestion has been applied in many wireless network circumstances, for example, WSN [

Lyapunov-Krasovskii functionals and Linear Matrix Inequalities (LMIs) method are usually proposed to control network congestion. In [

Figure

A typical scenario of WSDN with the propagation delay

Our goal is to maximize the global network throughput by stability control and keep the global network parameters stable at this optimal state by robust control with propagation delay and external interference. The propagation delay is denoted by

The padding waiting time is a key network parameter for robust control in WSDNs. As shown in Figure

The padding waiting time for robust control in WSDNs.

The closed-loop WSDN may be classified into two parts, which are analyzed in the following subsections.

A novel nonpreemptive scheduling scheme is proposed, which can be prearranged to stabilize the network parameters of each forwarding device. In order to tackle network congestion problem, in a scheduling problem, one has to find the minimization of the sum of the padding waiting time under the given constraints. Appropriate padding waiting times are arranged for each forwarding device. There exists an optimized scheduling scheme in each forwarding device. The schemes together implement the stability control for network congestion and maximize the global network throughput.

There are

Each point-to-point network transmission

Above all, the following arrangement variables is introduced to propose a mathematical description

For each arrangement

The padding waiting times can be arranged under the constraints before transmission. At the beginning, the optimized problem of minimizing the sum of the padding waiting time can be easily solved and the arrangement proportion is uncomplicated calculated as

However, propagation delay and external interference in wireless environments may cause the network unstable. Therefore, the robust control problem is considered to maintain network stability in the presence of propagation delay and external interference.

Briefly speaking, when a network transmission service enters the WSDN or it is generated in a forwarding device, it is queued in the buffer and waits for processed and transmitted. If the communication medium becomes free, the scheduling scheme could be nonpreemptively implemented for establishing an end-to-end path in the centralized controller after receiving the advertisements from the forwarding devices. The controller designs the control policy by means of the scheduling scheme and then sends control instructions to adjust the padding waiting time in each forwarding device.

With propagation delay and external interference, the current state

According to analyzing the propagation delay in the closed-loop WSDN, the propagation delay from forwarding device to the centralized controller (DC) and the reversed one (CD) are defined as

The forwarding devices continually adjust their padding waiting times following the control instructions. Thus, the network services in the forwarding devices constantly achieve nonpreemptive scheduling by means of the advertisements (a packet-in message).

First, the forwarding devices advertise the error state of the network service

Thus, the control command

The external interference in this paper is defined as the interference of the duration. Therefore, the external interference is considered as a kind of additive interference, which may lengthen the padding waiting times in the forwarding devices. Then, the closed-loop network model can be formulated into a robust

Thus, the robust

According to the term (

For given two positives

The closed-loop WSDN (

Given constant matrices

In the following, let

Consider the robust

We firstly define

In the closed-loop network, the Lyapunov-Krasovskii functionals can be expressed by

For any appropriate dimension matrix

For an appropriate dimension matrix

Thus, from (

Defining

Considering

Sum

Based on the Lyapunov-Krasovskii functionals, the robust

The proof is complete.

The parameters of desired robust

In this section, a numerical simulation is conducted to indicate the effectiveness of the proposed scheme in WSDNs and the control policies are designed given in Theorem

In actual WSDNs, QoS mechanism is the typical instance as the precedence order of network service contained integrated service and differentiated service. Usually, there are eight priority levels in the QoS mechanism, defined from 0 to 7 with 0 being the highest. Denote

According to Theorem

Suppose the control strength

Notably, the error states may increase or decrease based on the different initial state. However, the difference states

The variations of

The variations of

The final convergence of error states in Figures

This section introduces the design of the control policy based on the proposed scheme in WSDNs. We select the intermediate priority

The variations of

The variations of

Therefore, the appropriate adjustments of QoS control policy can easily be designed in the controller. The control policy can be designed to control the width measurement under different initial error states.

This paper have adopted robust control to tackle the problems of maximizing network throughput and keeping the network stable during congestion control in WSDNs. Firstly, an efficient nonpreemptive scheduling scheme has been proposed to maximize the global network throughput. Secondly, a robust control model with propagation delay and external interference is presented by using Lyapunov-Krasovskii functionals. The sufficient conditions have been formulated by LMIs. Finally, the numerical simulation has been conducted to indicate the effectiveness of the proposed scheme.

Future studies should explore the impact of implementation delays and stochastic external interference on the performance of robust control for network congestion in WSDNs. Delays are ubiquitous in wireless networks while frequently causing stability problems. The approach that we have presented would be extended to develop more complex algorithms and be applied in other wireless fields.

The authors declare that they have no competing interests.

This work is supported by the 863 project (Grant no. 2014AA01A701); the National Natural Science Foundation of China (Grant nos. 61271168, 61471104).