Mobile Information Systems

Volume 2016 (2016), Article ID 3297938, 8 pages

http://dx.doi.org/10.1155/2016/3297938

## Optimization of Access Threshold for Cognitive Radio Networks with Prioritized Secondary Users

School of Computer and Communication Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China

Received 29 January 2016; Accepted 1 June 2016

Academic Editor: Carlos Pomalaza-Ráez

Copyright © 2016 Yuan Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We propose an access control scheme in cognitive radio networks with prioritized Secondary Users (SUs). Considering the different types of data in the networks, the SU packets in the system are divided into SU1 packets with higher priority and SU2 packets with lower priority. In order to control the access of the SU2 packets (including the new arrival SU2 packets and the interrupted SU2 packets), a dynamic access threshold is set. By building a discrete-time queueing model and constructing a three-dimensional Markov chain with the number of the three types of packets in the system, we derive some performance measures of the two types of the SU packets. Then, with numerical results, we show the change trends for the different performance measures. At last, considering the tradeoff between the throughput and the average delay of the SU2 packets, we build a net benefit function to make optimization for the access threshold.

#### 1. Introduction

In conventional cognitive radio networks, two types of users, namely, Primary Users (PUs) and Secondary Users (SUs), share the spectrum resource in the system. The SUs can occupy the spectrum when the spectrum is not occupied by the PUs. The PUs have higher priority than the SUs and the PUs can interrupt the transmission of the SUs to take over the spectrum [1]. Most of existing researches for cognitive radio networks were studied under the assumption of single type of SUs [2–4]. However, in practical networks, there are different types of data in the system. So, it is necessary to consider the different types and prioritization among the SUs in cognitive radio networks.

In recent years, some researches began to focus on the performance analysis of the cognitive radio networks with prioritized SUs.

Lee et al. considered a cognitive radio network with three types of calls, namely, PU call, SU1 call, and SU2 call, in the system [5]. They denoted the high priority and the low priority SU calls as SU1 calls and SU2 calls. By building a continuous-time Markov chain and applying the Gauss-Seidel method, they gave the steady-state probability distribution of the system. Moreover, they presented some performance measures, such as the blocking rate and the throughput of the SU2 call.

Zhang et al. analyzed the transmission delay of priority-based SUs in the opportunistic spectrum access (OSA) based cognitive radio networks [6]. By employing a preemptive resume priority (PRP) M/M/1 queuing model, they derived some performance measures, such as the transmission delay of the interrupted SUs with each priority level and the overall transmission delay of the interrupted SUs.

Zhao and Yue considered cognitive radio networks with multiple SUs [7]. A nonpreemptive priority scheme for the SU packets with higher priority was proposed and compared with the preemptive priority scheme. By constructing and analyzing a three-dimensional Markov chain, they derived the expression for the interrupted rate of the two types of SU packets, respectively.

However, the above researches about cognitive radio networks with prioritized SUs did not consider the access control for the SU packets with lower priority. In cognitive radio network, larger number of SU packets with lower priority which access the system without any restriction will disturb the transmission of the PUs and the SUs with higher priority. So, it is necessary to control the access of the SU packets with lower priority reasonably. In this paper, we consider setting an access threshold for the SU packets with lower priority (called SU2 packets) to control the access of the SU2 packets. Specially, we also make optimization for the access threshold, while the optimization research was not shown up in [5–7].

On the other hand, we can find that the researches about cognitive radio networks with priority SUs mentioned above were analyzed by using continuous-time models. However, considering the digital nature of model networks, the discrete-time models are more suitable when analyzing the system performance of the networks [8]. So, in this paper, we evaluate the system performance of the proposed cognitive radio networks with the discrete-time queueing analysis. By building a discrete-time queueing model with multiple priority levels, we construct a three-dimensional Markov chain and give the transition probability matrix of the Markov chain. Then with the obtained steady-state distribution, we derive some performance measures of the system. At last, we make optimization for the access threshold by building a net benefit function.

The remainder of this paper is organized as follows. The system model with model assumption and model analysis is demonstrated in Section 2. In Section 3, different performance measures for the SU1 packets and the SU2 packets are derived, respectively. In Section 4, numerical results for different performance measures are shown. Considering the tradeoff between different performance measures, the optimization for the access threshold is given in Section 5. Finally, conclusions are drawn in Section 6.

#### 2. System Model

##### 2.1. Model Assumption

We focus on a cognitive radio network with a single channel. The PU packets have higher priority to occupy the channel than the SU packets. There are two types of SU packets, namely, SU1 packets and SU2 packets. We assume that the SU1 packets have higher priority than the SU2 packets. That is to say, the PU packets have the highest priority, and the SU2 packets have the lowest priority. The PU packets can interrupt the transmission of the SU1 packets and the SU2 packets, while the SU1 packets can interrupt the transmission of the SU2 packets.

In order to reduce the latency of the PU packets and the SU1 packets, no buffers are set for the PU packets and the SU1 packets.

When a PU packet arrives at the system, if the channel is occupied by another PU packet, this newly arriving PU packet will leave the system to find another available channel directly. If the channel is occupied by an SU packet (an SU1 packet or an SU2 packet), this newly arriving PU packet will interrupt the transmission of the SU packet and occupy the channel.

When an SU1 packet arrives at the system, if the channel is occupied by a PU packet or an SU1 packet, this newly arriving SU1 packet will also leave the system to find another available channel. If the channel is occupied by an SU2 packet, this newly arriving SU1 packet will interrupt the transmission of the SU2 packet and occupy the channel.

A buffer called SU2 buffer is prepared for the SU2 packets. In order to control the access of the SU2 packets, an access threshold is set for the SU2 packets. When an SU2 packet arrives at the system, if the number of SU2 packets in the SU2 buffer is equal to the access threshold, this SU2 packet will be blocked by the system. The access threshold can also control the return action of the interrupted SU2 packet. When the transmission of an SU2 packet is interrupted, if the number of SU2 packets in the SU2 buffer is smaller than the access threshold, this interrupted SU2 packet can return back to the SU2 buffer; otherwise, this interrupted SU2 packet has to leave the system. Specially, we assume that the interrupted SU2 packets have higher priority than the newly arriving SU2 packets.

Based on the access control scheme mentioned above, we can build a queueing model with multiple priority levels and finite waiting room.

Considering the digital nature of modern networks, the time axis is assumed to be divided into slots with equal size. The slot boundary is denoted as . The arrival intervals of the PU packets, the SU1 packets, and the SU2 packets are assumed to follow geometric distribution with arrival rates , , and . The transmission time of the PU packets, the SU1 packets, and the SU2 packets is assumed to follow geometric distribution with service rates , , and . The access threshold is denoted as , where .

Let be the total number of packets (including PU packets, SU1 packets, and SU2 packets) in the system at the instant . Let be the number of SU1 packets in the system at the instant . Let be the number of PU packets in the system at the instant . We note that constitutes a three-dimensional discrete-time Markov chain. With the access threshold , we can give the state space of as follows:

##### 2.2. Model Analysis

Let be the state transition probability matrix for the three-dimensional Markov chain . can be given as a block-structured matrix as follows:

Hereafter, we use the overbar notation to denote the probability of the complement of an event, for instance, . Moreover, we denote , . The elements of can be discussed by following subblock matrices.

is the probability for the total number of packets in the system being fixed at . can be given as follows:

is the transition probability subblock when the total number of packets in the system transfers from to . can be given as follows:

is the transition probability subblock when the total number of packets in the system transfers from to . can be given as follows:

is the transition probability subblock when the total number of packets in the system transfers from to . can be given as follows: where describes the transpose operator of the matrix.

is the transition probability subblock when the total number of packets in the system transfers from to , where . can be given as follows:

is the transition probability subblock when the total number of packets in the system transfers from to , where . can be given as follows:

is the transition probability subblock when the total number of packets in the system transfers from to , where . can be given as follows:

is the transition probability subblock when the total number of packets in the system transfers from to . can be given as follows:

is the transition probability subblock when the total number of packets in the system is fixed at . can be given as follows:

The structure of the transition probability matrix indicates that the three-dimensional Markov chain is nonperiodic, irreducible, and positive recurrent [9]. The steady-state distribution of the three-dimensional Markov chain is defined as follows:

Let be the steady-state probability vector, which is the unique solution of equations , , where is a one column vector.

We partition as , where and for . By applying a Gauss-Seidel method, we can obtain the steady-state probability vector .

#### 3. Performance Measures

##### 3.1. Performance Measures of the SU1 Packets

The average queue length of the SU1 packets is defined as the number of SU1 packets in the system per slot. We can give the expression of the average queue length of the SU1 packets as follows:

The blocking rate of the SU1 packets is defined as the number of SU1 packets that are blocked by the system per slot. We can give the expression of the blocking rate of the SU1 packets as follows:

The interrupted rate of the SU1 packets is defined as the number of SU1 packets that are interrupted by the PU packets per slot. We can give the expression of the interrupted rate of the SU1 packets as follows:

The throughput of the SU1 packets is defined as the number of SU1 packets that are transmitted completely by the system per slot. We can give the expression of the throughput of the SU1 packets as follows:

##### 3.2. Performance Measures of the SU2 Packets

The average queue length of the SU2 packets is defined as the number of SU2 packets in the system per slot. We can give the expression of the average queue length of the SU2 packets as follows:

The blocking rate of the SU2 packets is defined as the number of SU2 packets that are blocked by the system per slot. We can give the expression of the blocking rate of the SU2 packets as follows:

The interrupted losing rate of the SU2 packets is defined as the number of SU2 packets that are interrupted by the PU packets or the SU1 packets and being forced to leave the system because of the number of SU2 packets in the buffer achieving the access threshold. We can give the expression of the interrupted losing rate of the SU2 packets as follows:

The throughput of the SU2 packets is defined as the number of SU2 packets that are transmitted completely by the system per slot. We can give the expression of the throughput of the SU2 packets as follows:

The average delay of the SU2 packets is defined as the average time length from an SU2 packet joining the system to this SU2 packet leaving the system (being transmitted completely or being interrupted to leave). With Little’s formula [10], we can give the expression of the average delay of the SU2 packets as follows:

#### 4. Numerical Results

In this section, we show the change trends for different performance measures with numerical results for the SU1 packets and the SU2 packets, respectively.

##### 4.1. Numerical Results for the SU1 Packets

According to the working principle of the system model, the performance of the SU1 packets will be influenced by the PU packets. Figures 1–3 show the change trends for the average queue length , the blocking rate , and the throughput of the SU1 packets with different parameter settings of PU packets and SU1 packets.