Mobile Information Systems

Volume 2016 (2016), Article ID 8981251, 16 pages

http://dx.doi.org/10.1155/2016/8981251

## Energy-Efficient Transmission Strategy by Using Optimal Stopping Approach for Mobile Networks

^{1}College of Electrical Engineering, Guangxi University, Nanning 530004, China^{2}School of Computer and Electronic Information, Guangxi University, Nanning 530004, China

Received 18 September 2015; Revised 15 January 2016; Accepted 16 February 2016

Academic Editor: Qi Wang

Copyright © 2016 Ying Peng 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

In mobile networks, transmission energy consumption dominates the major part of network energy consumption. To reduce energy consumption for data transmission is an important topic for constructing green mobile networks. According to Shannon formula, when the transmission power is constant, the better the channel quality is, the greater the transmission rate is. Then, more data will be delivered in a given period. And energy consumption per bit data transmitted will be reduced. Because channel quality varies with time randomly, it is a good opportunity for decreasing energy consumption to deliver data in the best channel quality. However, data has delay demand. The sending terminal cannot wait for the best channel quality unlimitedly. Actually, sending terminal has to select an optimal time to deliver data before data exceeds delay. For this, this paper obtains the optimal transmission rate threshold at each detection slot time by using optimal stopping approach. Then, sending terminal determines whether current time is the optimal time through comparing current transmission rate with the corresponding rate threshold, thus realizing energy-efficient transmission strategy, so as to decrease average energy consumption per bit data transmitted.

#### 1. Introduction

Widespread deployment of mobile networks, for example, mobile ad hoc networks and mobile social networks, and rapid development of data services have brought about exponential growth of wireless mobile terminals (MTs) and dramatic increase of energy consumption in mobile networks. However, the batteries of MTs offer very limited energy and lack the capacity for sustainable supply, especially in the case of inadequate network infrastructure or on the move. As energy consumption greatly affects mobile users, it is highly necessary to make efficient use of resources of mobile networks and reduce energy consumption of MTs for improving mobile users’ satisfaction. It is an important and urgent subject to be solved for the construction of green mobile computing [1, 2].

In mobile networks environment, combined influence of multipath propagation, user on the move and channel fading, and so forth will bring about rapid fluctuations in capacity and quality of wireless channel with the change of time. If wireless networks always dynamically allocate resources to the channel in the best instantaneous state or MTs always choose the time of the best channel quality to transmit data, the utilization ratio of wireless network resources will be greatly increased and the performance of network is improved. MT delivers data efficiently using the feature of channel quality varying with time. This strategy is named as opportunistic scheduling [3].

There are two types of opportunistic scheduling, which include centralized opportunistic scheduling and distributed opportunistic scheduling. The former assumes the existence of a central scheduler, which can detect current status of all channels in the network and schedule operation and processing in a centralized manner. The latter, without knowing channel status of other devices, accesses and competes for channel in random mode and certain probability. After obtaining the channel through competition, it will either deliver data immediately if in good quality channel or give up and compete again if in bad quality channel, thus realizing full utilization of network resources in good quality channel.

The distributed opportunistic scheduling technique can take full advantage of device diversity of multiple users and the differences of channel in different time. In order to increase efficiency of the whole network, distributed opportunistic scheduling permits users to make decision after their temporary surveillance on channel. There is no such need of a complex control center and real time information of all channels’ quality. In addition, this technique can decrease network energy consumption [4–8] and enhances network performance [9–12], for example, delivery ratio and throughput.

If the transmission power of sending terminal (ST) is given in wireless link, the greater the transmission rate is, the more data the ST can transmit within the same time period. Consequently, average energy consumption per unit data transmitted (AECPUDT) is smaller. However, transmission rate changes with the wireless channel quality fluctuations. If ST selects the time when channel is in good state to send data, the higher the transmission rate is, the lower the AECPUDT will be. Therefore, in order to minimize AECPUDT on the link, ST needs to survey channel condition timely and then chooses good channel quality time to transmit in accordance with present amount of data accumulated. ST chooses better channel quality for data delivery using the nature of channel quality changing with time, which is called distributed opportunistic scheduling [4–12]. In order to obtain an optimal energy efficiency time (i.e., AECPUDT is smallest) to deliver data, ST continuously surveys channel condition in distributed opportunistic scheduling. Therefore, the distributed opportunistic scheduling could be transformed into an optimal stopping rule strategy to be proved. In this strategy, the decision maker (ST) obtains the time of the minimal expected cost (average energy consumption) to stop observation, based on the continuous observation toward random variable (channel quality), and then takes special actions (transmitting data) to achieve the objective of minimal expected cost.

For the energy consumption problem research in [5], authors of that paper assumed that ST always had enough cumulative data and used the maximum transmission power at the maximum delay and then derived every transmission power threshold of each transmission slot time before the delay. Since current cumulative data quantity of ST is not taken into consideration of these thresholds, ST could neither achieve the optimal energy efficiency under different cumulative data quantity nor guarantee the data delivery ratio (i.e., the ratio of the amount of data transmitted to the total amount of data cumulated). In this paper, the authors take the amount of data cumulated in ST as related factor for selecting the optimal transmission time. In order to better derive the optimal stopping rule, it is assumed that the data generation rate of ST is given, which is consistent with reality needs. For example, when ST transmits some online data, the amount of data to be transmitted per unit time is identified. In addition, the rate of ST obtaining data to be forwarded is also assumed to be constant in [6, 7]. Inspired by optimal stopping theory, the proposition of energy-efficient transmission strategy in this paper is based on the following ideas. When delay requirement and data generation rate on wireless link are given, the matter of distributed opportunistic scheduling about ST selecting optimal channel quality is turned into an optimal stopping problem. Then, the optimal threshold of transmission rate at every selection slot time is acquired based on the optimal stopping theory. Finally, the optimal rate time to transmit data is chosen, thus reducing the AECPUDT and increasing data delivery ratio.

The remaining part is arranged as follows. Related research work of other scholars is reviewed in Section 2. Section 3 describes system model and optimization problem. Then, the energy-efficient transmission strategy using optimal stopping approach is proposed in Section 4. Section 5 presents simulation results and analysis. Finally, Section 6 concludes this paper and prospects future work.

#### 2. Related Research Work

At present, opportunistic scheduling based on time-varying wireless channel quality is widely researched and applied to mobile networks, such as mobile ad hoc networks and mobile social networks. These researches are mainly centered on selection of the optimal transmission time, aiming to improve network performance and energy efficiency of the three scenarios, namely, multiple devices and multiple channels, multiple devices and single channel, and single device and single channel. Researchers mainly focus on two optimization objectives, which are to improve energy efficiency [4–8, 13–16] and to increase network throughput [9–12].

(1) For reducing network energy consumption, many scholars utilize method of choosing the optimal time of channel quality to transmit so as to reduce energy consumption of data transmission [4–8, 13]. Others pay attention to energy consumption saving in the entire routing [14–16].

In order to decrease energy consumption for data transmission, the authors in [4, 5] studied how to choose optimal transmission time to improve energy efficiency in the environment of multiple devices and single channel as well as single device and single channel, respectively. The authors constructed an infinite horizon stopping problem based on optimal stopping theory in [4]. When the competing probability of multiple STs is given in homogeneous environment, the optimal threshold of transmission rate can be derived, which effectively optimized energy efficiency of network. They also proposed a heuristic method for heterogeneous scenario. But they did not consider the data transmission delay demand. The authors considered the case of data with the maximum transmission delay demand in [5]. They studied the transmission energy consumption optimization problem where channel quality varies with time. After obtaining the optimal threshold of power at each slot time using optimal stopping method, ST chose the optimal channel quality time to transmit data, thus energy consumption saved and delay guaranteed. According to their assumption, ST had adequate data to transmit all the time, which is an ideal case. In true applications, ST may have much more or much less data to deliver during the transmission period, while ST obtains excellent opportunities to transmit. The authors in [6] studied the cost optimization of that roadside unit transmitting data to passing-by vehicle in vehicle delay tolerant network. By introducing a function of transmission cost and a penalty cost for exceeding delay, they proved that the time when the queueing delay at roadside unit is above certain threshold is an optimal one for roadside unit to deliver data flow. The simulation results show that the optimal stopping theory can effectively save transmission cost of roadside unit. Furthermore, in [7] they studied this problem and gave a more complete theoretical derivation and experimental proof. We proposed an energy consumption optimization strategy for data transmission in [8] and formed preliminary ideas of utilizing optimal stopping approach to save energy. We present more perfect theoretical derivation and abundant experimental proof in this paper, which includes five points mainly. The first is the full explanation of opportunistic scheduling problem using optimal stopping theory. The second is the detailed related research work and the differences between ours and the work of others in [5]. The third is the correlation between this work and optimal stopping theory. The fourth is the detailed solution and performance analysis of the strategy. The fifth is the relationship of optimal energy efficiency and parameters and analysis of average scheduling period. The problem of choosing good channel with delay constraint in mobile networks is studied by authors of [13]. They utilized stochastic game to obtain the optimal power threshold for successful data transmission in opportunistic scheduling, which reduced the waste of energy caused by channel error and packet collision.

In addition, some others focused on saving energy in the opportunistic network, which is consumed by sending information from source to destination. Due to rapid fluctuation of channel condition, routing information estimated by average channel quality will become out of date, but opportunistic routing can avoid this case. Compared with the traditional way that data is delivered through a predefined end-to-end path, opportunistic routing enables data to be transmitted from source to destination without end-to-end path. For example, [14] proposed a method of cooperative communication for energy efficiency. The authors fully exploited the random change nature of wireless channel and enabled data packet to be transmitted through better path by high energy efficiency relay node. Consequently, energy consumption is reduced. In [15], they introduced the functions of computing end-to-end energy consumption for traditional routing and opportunistic routing. The authors utilized the technique of cross-layer information exchange to reduce energy consumption and designed energy-efficient routing algorithms based on Dijkstra algorithm. The simulation results show that energy-efficient opportunistic routing outperforms the traditional routing. We in [16] proposed the routing strategy of minimizing transmission energy consumption in mobile network, where transmission delay demand of data is considered. The routing strategy decreased network energy consumption effectively.

(2) For increasing network throughput of opportunistic network, researchers propose all kinds of schemes and algorithms to select a good channel for data transmission, so as to obtain more desirable transmission rate and increase data delivery ratio.

In order to improve network throughput in an ad hoc network where many links contend for the same channel by random access, two distributed opportunistic scheduling strategies from the network-centric and user-centric perspective are proposed in [9], respectively. In [10], the authors studied the improvement of network throughput with proportional fairness. In the scenario of multiple devices competing for the same channel, the researchers constructed block fading channel model with different channel detection slot time dependencies in [11]. Taking into account the impact of channel dependencies on transmission scheduling and system performance, they formulated optimal stopping problem of finite horizon and chose the effective decision time, then characterized the system performance by backward induction, and finally solved the problem by recursive algorithm and effectively enhanced throughput of the system. Considering secure and regular links coexisting in a mobile network, [12] designed a QoS-oriented distributed scheduling scheme based on optimal stopping theory to maximize the whole network throughput.

In summary, for the distributed opportunistic scheduling, it is a very important solution to obtain the optimal scheduling time [4–12] using the optimal stopping theory. In these researches including multiple devices competing to select multiple channels, multiple devices competing to select single channel, and single device selecting single channel, researchers constructed different kinds of optimal rule problem. They solved these problems to obtain the optimal transmission rate threshold [4, 8–11], the optimal power threshold [5], and the optimal transmission time [6, 7], respectively, so as to minimize energy consumption [4–8] or maximize network throughout [9–12]. We research the energy-efficient transmission strategy in this paper, when one device selects single channel. Differing from the hypothesis in [5] that ST has adequate data all the time, we assume that data is generated at a certain rate. In addition, the objectives of minimizing expected energy consumption and average energy consumption per unit time are studied in [5]. This paper considers the objective of minimizing AECPUDT, under the constraint condition of finishing transmitting all data accumulated. For this purpose, we construct the minimization problem of AECPUDT with transmission delay demand and the amount of data transmitted constraint. This minimization problem can be turned into a finite horizon optimal stopping rule problem, so as to acquire the optimal transmission rate thresholds. This paper includes the following two main contributions. (1) The transmission energy consumption optimization problem with transmission delay demand and the amount of data transmitted constraint in mobile network is studied using the characteristics of channel quality varying with time. The effect of the given data generation rate and transmission delay on the AECPUDT is analyzed. (2) We construct the finite horizon optimal stopping rule problem about the minimal AECPUDT under amount of data transmitted constraint. Then, the optimal threshold of transmission rate at every slot time is obtained, thus forming the energy-efficient transmission strategy using optimal stopping approach.

#### 3. Theoretical Background and Problem Description

##### 3.1. System Model

In our mobile networks model, we assume that MT accesses channel using Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) protocol. When data needs to be transmitted between two MTs, after establishing the wireless link within transmission range, MT will choose good channel to transmit data immediately. The research purpose of this paper is to minimize the AECPUDT in wireless link under the demand of transmission delay. Meanwhile, the delivery ratio of data transmission must be guaranteed.

In mobile networks, we assume that time is divided into certain slot periods (s). The channel gain submits some probability distribution (such as Rayleigh model fading) and remains unchanged in period [4, 5, 9, 11] on the wireless link construed by ST and a receiving terminal (RT). The data generation rate is (bit/s). ST delivers the data to the RT within the transmission delay using transmission power (W). To obtain real time information of channel quality, RT transmits a short signal to ST every period [5]. Then, ST estimates channel quality according to the signal’s power. This consumes energy (J) for each detection. Each duration of detection signal is extremely short and far less than . After the ST discovers channel in good condition, it will send data during period . (J) is the energy consumption for data transmission and far bigger than . Because the channel gain keeps constant in period , is satisfied. This entire process from the starting of channel detection to the end of data transmission is called a round of channel detection and data transmission. Its process is given in Figure 1. In a round of detection, the total duration for detection is (s), and the total energy consumption for detection is (J). Here, is the number of detection instances, which is counted from the end of previous round of data transmission. For the first round, the initial counting of is 0. If transmission rate is (bit/s), ST can transmit (bit) data in a round. If there is , ST does not transmit all cumulated data and the remaining data is bits. If , ST actually transmits bits’ data. Furthermore, when is satisfied, ST wastes power due to being idle in part of duration . Obviously, ST can increase the amount of data transmitted in given transmission duration by selecting the time of greater transmission rate, thus decreasing the AECPUDT and improving energy efficiency. Shannon formula is presented in the following expression: