Mobile Information Systems

Volume 2016, Article ID 2426580, 10 pages

http://dx.doi.org/10.1155/2016/2426580

## Social Optimization and Pricing Policy in Cognitive Radio Networks with an Energy Saving Strategy

^{1}College of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China^{2}Key Laboratory for Computer Virtual Technology and System Integration of Hebei Province, Yanshan University, Qinhuangdao 066004, China^{3}National Center for Public Cultural Services, Ministry of Culture of China, Beijing 110000, China

Received 10 January 2016; Accepted 7 June 2016

Academic Editor: George Ghinea

Copyright © 2016 Shunfu Jin 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

The rapid growth of wireless application results in an increase in demand for spectrum resource and communication energy. In this paper, we firstly introduce a novel energy saving strategy in cognitive radio networks (CRNs) and then propose an appropriate pricing policy for secondary user (SU) packets. We analyze the behavior of data packets in a discrete-time single-server priority queue under multiple-vacation discipline. With the help of a Quasi-Birth-Death (QBD) process model, we obtain the joint distribution for the number of SU packets and the state of base station (BS) via the Matrix-Geometric Solution method. We assess the average latency of SU packets and the energy saving ratio of system. According to a natural reward-cost structure, we study the individually optimal behavior and the socially optimal behavior of the energy saving strategy and use an optimization algorithm based on standard particle swarm optimization (SPSO) method to search the socially optimal arrival rate of SU packets. By comparing the individually optimal behavior and the socially optimal behavior, we impose an appropriate admission fee to SU packets. Finally, we present numerical results to show the impacts of system parameters on the system performance and the pricing policy.

#### 1. Introduction

With the explosive growth of wireless application, one of the hot topics of research is how to improve the spectrum efficiency as well as reduce the communication consumption. Cognitive radio is a recent and promising development in wireless communications technology [1]. Green energy powered cognitive radio networks (CRNs) are capable of liberating wireless communications from spectral and energy constraints [2].

One of the key challenges in wireless networks is how to control the base station (BS) in order to decrease the energy consumption. In addition, we should also focus on how to ensure the Quality of Service (QoS) of end users and spectrum efficiency. From the related literature, we find that the main method to release the energy constraint is sleep mode, by which communication power can be reduced when the BS is at the sleep state [3, 4]. We also find that the cognitive radio technology has been studied as an effective solution to alleviate the limitation of the spectrum resource [5]. In addition, in order to achieve the maximum value of social profit of the system, people pay more and more attention to the behaviors of the data packets, including the individually optimal behavior and the socially optimal behavior [6, 7].

In this context, we firstly introduce an energy saving strategy with sleep mode in CRNs. The proposed strategy highlights how the BS is switched between the sleep state and the awake state to achieve the trade-off between the energy saving effect and the response performance. In addition, we assess the system performance by constructing a Quasi-Birth-Death (QBD) process model and validate the analytical results with simulations. According to a natural reward-cost structure, we analyze the individually optimal behavior and the socially optimal behavior of the energy saving strategy and use an optimization algorithm based on standard particle swarm optimization (SPSO) method to search the socially optimal arrival rate of secondary user (SU) packets. By comparing the individually optimal behavior and the socially optimal behavior, we impose an appropriate admission fee to SU packets.

The remainder of this paper is organized as follows. In Section 3, we describe an energy saving strategy with sleep mode and system model, and then we carry out the stability condition of the system. In Section 4, we analyze the model and derive the formulas for the performance measures. In Section 5, we demonstrate the influence of system parameters on the system performance with numerical results. In Section 6, through theoretical analysis and numerical comparison of the individually optimal behavior and the socially optimal behavior of the energy saving strategy, we impose an appropriate pricing policy. Finally, we summarize the conclusions in Section 7.

#### 2. Related Works

In wireless networks, sleep mode is one of key techniques to reduce energy consumption. One important way to address the energy saving problem is to introduce sleep mode to the BS. Dini et al. studied the sleep mode as an approach to decrease the energy consumption in BS of long term evolution (LTE) heterogeneous networks (HetNets). Furthermore, they introduced two sleep algorithms, namely, single-sleep and multiple-sleep, to determine the time instant to enable micro- or pico-BSs to employ sleep mode [3]. Rengarajan et al. characterized the maximum energy saving that can be achieved in a cellular wireless access network with sleep mode under a given performance constraint. By taking into account the QoS perceived by end users, their approach allows the derivation of more realistic estimates that can be used to evaluate the efficacy of schemes utilizing sleep modes to save energy [4]. Li et al. proposed a new sleep mechanism called sleep-transmit mode (STM) that provides a solution by adding a transmit state to the currently employed mechanism in passive optical network (PON) standards. When compared to interrupted sleep mode, STM achieves up to 29% power reduction while providing comparable delay performance for upstream packets [8]. Some authors used a Markov chain technique to evaluate the energy savings with the sleep mode mechanism in a single user terminal [9, 10]. In contrast to [9, 10], we are more concerned with the sleep mode on the BS (rather than that on the user terminal). In [11], Premalatha et al. took a survey on energy saving methods for green communication networks and found that sleep mode is adapted for reducing the energy consumption of BS.

Recently, the opportunistic spectrum access mechanism in CRNs has been paid more attention to make the spectrum scarcity less severe that wireless communications face now. Cognitive radio is a form of wireless communication in which a transceiver can intelligently detect the communication channels which are in use and which are not and instantly move into unused channels while avoiding occupied ones [12]. Cognitive radio is widely considered to resolve the scarcity of spectrum bands and to meet the burgeoning requirements of wireless services by employing opportunistic spectrum sharing [13]. In [14], Anwar et al. proposed a new optimization-based access strategy of multipacket reception (MPR) channel for multiple SUs accessing the primary user (PU) spectrum. The concept of CRNs is regarded as a prosperous technology duo to high spectrum efficiency [12–14]. In addition to efficient spectrum usage, how to reduce energy consumption is the current problem to be solved. An energy harvesting CRN design will not only ease the spectrum shortage problem, but also result in a green design [15]. Most of the existing dynamic spectrum access (DSA) schemes only consider the SUs’ transmission in licensed spectrum without considering the unlicensed bands. In order to reduce dropping and blocking probabilities of SUs, the researchers extended classical schemes, including random access scheme and reservation based channel access scheme [16].

The application of game theory in performance optimization is becoming more and more widespread and important. Cuong et al. studied a noncooperative game problem for* M/M/1* queueing control in the cognitive radio system. In queueing game with server breakdowns, each customer wants to optimize its benefit in a selfish distributed manner [17]. Zheng et al. proposed a distributed cooperative framework to improve the energy efficiency of green cellular networks. Based on the traffic load, neighboring BSs cooperate to optimize the BS switching (sleeping) strategies so as to maximize the energy saving while guaranteeing users’ minimal service requirements [18]. Li and Han studied the individually and socially optimal strategies based on queueing control in cognitive radio systems. The study result reveals that the individually optimal strategy does not yield the socially optimal one. To bridge the gap between the individually and socially optimal strategies, a pricing mechanism is proposed to toll the service of each SU [7]. In CRNs, Tran et al. studied price-based spectrum access control, which characterized network operators’ service provisions to delay-sensitive SUs via pricing strategies [19].

#### 3. Energy Saving Strategy with Sleep Mode and Model Description

##### 3.1. Energy Saving Strategy with Sleep Mode

In CRNs, the PU has high priority to occupy the spectrum. If the spectrum sensing results are perfect, the transmission of a PU packet will not be influenced by SU packets, while interrupting the transmission of an SU packet by PU packets is possible. The SU packet will queue at the head of the buffer for future transmission.

The BS in conventional CRNs is always awake even though there are not any packets, either PU packet or SU packet, to be transmitted or received. In this paper, we describe an energy saving strategy. In order to reduce the energy consumption, the BS will be switched into the sleep state from the awake state when the spectrum is idle and the buffer of SU packets is empty.

In the proposed energy saving strategy, the BS will be switched between two states, namely, sleep state and awake state, respectively.(1)During the sleep state, the BS will wake up for a short time at every boundary of the time slot to listen whether there is a packet arrival or not. If there is no packet arrival before the sleep timer expires, the BS will start another sleep period once the sleep timer is over. If a PU packet arrives at the system during the sleep state, the sleep timer will be stopped immediately, and the BS will be switched to the awake state. If there is no PU packet arrival but at least one SU packet arrival during the sleep state, the BS will be switched to the awake state once the sleep timer expires.(2)If the BS is in the awake state, all the packets will be transmitted continuously. PU packets will be transmitted with high priority, while SU packets will be transmitted opportunistically. When all the packets are transmitted completely, a sleep timer will be started and the BS will be switched to the sleep state.

We note that the energy consumption is lower when the BS is in the sleep state than that in the awake state. By this way, communication energy will be saved in CRNs with the sleep mode. As a cost of energy conservation, the SU packets will be delayed for longer time before transmission. It is necessary for us to evaluate and optimize the system performance mathematically.

##### 3.2. Model Description

We consider a CRN with a single licensed channel. The energy saving strategy proposed above is adopted by this system.

We consider a system model in discrete-time field. Time is assumed to be divided into fixed-length intervals, referred to as slots. The slots are marked as . We consider an early arrival system (EAS). In other words, we suppose that the arrival of data packets occurs at the beginning instant of a slot, marked as (, ), while the departure of data packets occurs at the end of instant of a slot, marked as (, ). We also assume that the data packets are transmitted within the slots, and the state transition of the BS occurs at the instant .

We assume that the arriving intervals of PU and SU packets follow geometric distributions with parameters and , respectively. In other words, the arrival rates of PU and SU packets are and , respectively. We assume that the transmission times of a PU packet and an SU packet follow geometric distributions with parameters and , respectively. Without loss of generality, we did not assume when describing the system model. PU packets are transmitted with pure loss and preemptive priority, while SU packets are transmitted with opportunity and interrupt retrial. In addition, we assume that the sleep timer length follows a geometric distribution with sleeping parameter .

Let be the total number of SU packets at the instant and let be the state of the BS at the instant ( means the BS is in the sleep state, means the BS is awake and a PU packet is being transmitted, and means the BS is awake and an SU packet is being transmitted). According to the above descriptions, a two-dimensional process composed of the total number of SU packets and the state of the BS is established. The state space of is given as follows:

Let be the probability that the number of SU packets is and the state of the BS is at the steady state. is given as follows:

Let be steady-state probability vector that the number of SU packets is . is given by

Let be the probability distribution of the system in steady state. is then given by

##### 3.3. Stability Condition

In the system considered in this paper, there are two types of packets, namely, PU packets and SU packets. When the total traffic load for both the PU packets and SU packets is less than , the system will reach a stable state.

We firstly address the traffic load of PU packets, which is defined as the probability that the BS is occupied by PU packets.

In CRNs, PU packets are transmitted with preemptive priority. Under the assumption that the spectrum sensing is perfect, the transmission of PU packets is independent of that of SU packets. Recall that once a PU packet arrives at the system, no matter the BS is in sleep state or not, the PU packet will be transmitted immediately. That is to say, the transmission of PU packets is also independent of the sleep mode. For this reason, the activities of PU packets can be modeled as a simple two-state Markov chain.

From the perspective of PU packets, the BS has two states, namely, idle state and busy state. The idle state means that the BS is not occupied by PU packets, while the busy state means that the BS is occupied by PU packets. Let be the probability that the BS is in idle state and let be the probability that the BS is in busy state. The BS changes to busy state from idle state with probability ; that is, there is an arrival of PU packet. The probability that the BS changes to idle state from busy state is ; that is, the PU packet is successfully transmitted, and no PU packet arrives at the system. We can get the balance equation and the normalization condition as

It is straight forward to derive and as follows:

From the definition of the traffic load of PU packets, we know that the traffic load of PU packets is the probability that the BS is in busy state. So

We define the traffic load of SU packet as the probability that the BS is occupied by SU packets. Since there is a buffer with infinite capacity for SU packets, no SU packets can be blocked. From the perspective of SU packets, once an SU packet enters the system, this SU packet will not leave the system until it is successfully transmitted. So the traffic load of SU packets is given as follows:

Combining (7) and (8), we can derive the total traffic load as follows:The stability condition of the system is shown as follows: that is,

We assume this stability condition to be fulfilled in the remainder of the paper.

#### 4. Model Analysis and Performance Measures

##### 4.1. Model Analysis

We define as the one step state transition probability matrix of the two-dimensional process . According to the number of SU packets, we give the one step state transition probability matrix in a block structure as follows:where The component matrix represents the case that the number of SU packets in the system changes to from . Particularly, we redefine three special cases that if , is denoted by , if , is denoted by , and if , is denoted by .

The structure of shows that the system transition occurs only in adjacent levels. Moreover, it is clear that the rows of the transition probability matrix are repeating after the third row. From the book written by Neuts [20], we know that the matrix has a block-tridiagonal structure which indicates that is a QBD process.

For the QBD process of the transition probability matrix , the necessary and sufficient condition of to be positive recurrence is that the matrix quadratic equationhas a minimal nonnegative solution and the spectral radius and the six-dimensional stochastic matrix has left invariant vector. When is positive recurrent, its stationary distribution satisfieswhere is a three-dimensional column vector with all elements being equal to one.

For analyzing this model, we need to find the minimal nonnegative solution of matrix (14). In fact, it is difficult to find an analytical solution for this system and therefore a numerical solution is required. In this case, we usually need to derive the recursion expression of the rate matrix .

Firstly, from (14), we derive the iterative expressions as follows:where is the th order approximation of and is the initial value of . Then, we can obtain by a recursive algorithm in Algorithm 1.

*Algorithm 1 (algorithm to obtain the minimal nonnegative solution ). * *Step 1*. Set the initial number of iterations by , the initial value by , the error precision , where is greater than , but infinitely close to . *Step 2*. Calculate the expression of by matrix (17). *Step 3*. Update by . **If **,** then **, goto Step . **else **. *Step 4*. Output .

With the help of the Matrix-Geometric Solution method and the recursive algorithm in Algorithm 1, we can get the steady-state probability defined in (2).

##### 4.2. Performance Measures

In this subsection, we derive two system performance measures in terms of the average latency and the energy saving ratio.

We first consider the average latency of SU packets, denoted by , which is defined as the time duration from the instant at which an SU packet joins the system to the instant that the SU packet is successfully transmitted. With Little’s formula, the average latency of SU packets is given as follows:

Next, we derive the energy saving ratio , which is defined as the reduction of the energy consumption per slot due to the introduction of the sleep mode. Energy is consumed normally in the awake state and is saved in the sleep state. Furthermore, additional energy will be consumed for each listening procedure in the proposed energy saving strategy. Therefore, the energy saving ratio is given as follows:where means the probability that the BS is not occupied, and are the energy consumptions per slot when the BS is in the awake state and the sleep state, respectively, and is the energy consumption for each listening procedure.

#### 5. Numerical Results and Discussions

In this section, we first describe our experiment environment and then discuss the numerical results. To investigate the system performance of CRNs with sleep mode for different sleeping parameters as well as the arrival rates of PU and SU packets, we take the parameters specified of the IEEE 802.11n in [21].

We assume that every IEEE 802.11n user independently generates its data packet. Referencing to [21], we set the parameters in Table 1.