# An Energy-Efficient MAC Protocol in Wireless Sensor Networks: A Game Theoretic Approach

- S. Mehta
^{1}and - K. S. Kwak
^{1}Email author

**2010**:926420

https://doi.org/10.1155/2010/926420

© S. Mehta and K. S. Kwak. 2010

**Received: **30 October 2009

**Accepted: **31 May 2010

**Published: **24 June 2010

## Abstract

Game Theory provides a mathematical tool for the analysis of interactions between the agents with conflicting interests, hence it is well suitable tool to model some problems in communication systems, especially, to wireless sensor networks (WSNs) where the prime goal is to minimize energy consumption than high throughput and low delay. In this paper, we use the concept of incomplete cooperative game theory to model an energy efficient MAC protocol for WSNs. This allows us to introduce improved backoff algorithm for energy efficient MAC protocol in WSNs. Finally, our research results show that the improved back off algorithm can improve the overall performance as well as achieve all the goals simultaneously for MAC protocol in WSNs.

## Keywords

## 1. Introduction

Communication in wireless sensor networks is divided into several layers. Medium Access Control (MAC) is one of those layers, which enables the successful operation of the network. MAC protocol tries to avoid collisions by not allowing two interfering nodes to transmit at the same time. The main design goal of a typical MAC protocols is to provide high throughput and QoS. On the other hand, wireless sensor MAC protocol gives higher priority to minimize energy consumption than QoS requirements. Energy gets wasted in traditional MAC layer protocols due to idle listening, collision, protocol overhead, and overhearing [1, 2]. There are some MAC protocols that have been especially developed for wireless sensor networks. Typical examples include S-MAC, T-MAC, and H-MAC [2–4]. To maximize the battery lifetime, sensor networks MAC protocols implement the variation of active/sleep mechanism. S-MAC and T-MAC protocols trades networks QoS for energy savings, while H-MAC protocol reduces the comparable amount of energy consumption along with maintaining good network QoS. However, their backoff algorithm is similar to that of the IEEE 802.11 Distributed Coordinated Function (DCF), which is based on Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) Mechanism. The energy consumption using CSMA/CA is high when nodes are in backoff procedure and in idle mode. Moreover, a node that successfully transmits resets it Contention Window (CW) to a small, fixed minimum value of CW. Therefore, the node has to rediscover the correct CW, wasting channel capacity, and increase the access delay as well. So, during the CSMA/CA mechanism, backoff window size and the number of active nodes are the major factors to have impact on the network performance and over all energy efficiency of MAC protocol. Hence, it is necessary to estimate the number of nodes in network to optimize the CSMA/CA operation. Furthermore, optimizing CSMA/CA operation is more challenging task for self-organizing and distributed networks as there are no central nodes to assign channel access in sensor nodes.

In sensor networks, each node has a direct influence on its neighboring nodes while accessing the channel. So, these interactions between nodes and aforementioned observations lead us to use the concepts of game theory that could improve the energy efficiency as well as the delay performance of MAC protocol. More on this will be discussed in section two of this paper.

Recently lots of researchers have started using game theory as a tool to analyze the wireless networks. Their game theoretic approaches were proposed to the wide area of wireless communication right from the security issues to power control, and so forth, [5–8]. To model WSNs problems into full information game theoretic problems is an extremely difficult task due to distributed nature of WSNs. In addition, full information sharing also results into additional energy and bandwidth consumption. So, we use the concept of incomplete cooperative game theory to solve the aforementioned challenges. In this paper, we present the basic idea of adjusting nodes' equilibrium strategy based on estimation of network conditions without full information. More details on this will be discussed in later part of this paper. To the best of our knowledge, there is very little work on the incomplete cooperative game theory in wireless networks. In [9, 10], authors used the concept of incomplete cooperative game theory in wireless networks for first time and proposed the G-MAC protocol for the same. However, their proposed scheme is not suitable for all traffic conditions, especially, nonsaturation traffic condition which is most likely in sensor networks. In [11] authors presented a virtual CSMA/CA mechanism to handle the nonsaturation traffic condition which is too heavy and complex for the sensor networks.

We also work on similar baseline and present our suboptimal solution for an energy efficient MAC protocol in wireless sensor networks. In short, the main contributions of this paper are as follows.

- (i)
To present an analytical model of energy efficient MAC protocol based on incomplete cooperative game theory.

- (ii)
To present a suboptimal solution for energy efficient MAC protocol in WSN.

- (iii)
To present a performance evaluation study for the proposed solution.

The rest of this paper is organized as follows. Game theory and the incomplete cooperative game are introduced in Section 2, respectively. In Section 3, we present an improve backoff algorithm to improve the energy efficiency of MAC protocol in WSNs. Finally, the concluding remarks and future works are given in Section 4.

## 2. Game Theory and Incomplete Cooperative Game

Game Theory is a collection of mathematical tools to study the interactive decision problems between the rational players (In rest of the paper, we keep using terms "node" and "player" interchangeably) (Here, it is sensor nodes). Furthermore, it also helps to predict the possible outcome of the interactive decision problem. The most possible outcome for any decision process is "Nash Equilibrium." A Nash equilibrium is an outcome of a game where no node (player) has any extra benefit for just changing its strategy one-sidedly [12, 13]. From last few years, game theory has gained a notable amount of popularity in solving communication and networking issues. These issues include congestion control, routing, power control, and other issues in wired and wireless communications systems, to name a few.

A wirless networking game.

Components of a game | Elements of a wireless network |
---|---|

Players | Nodes in the wireless network |

A set of actions | A modulation scheme, transmit power level, and so forth. |

A set of preferences | Performance metrics (e.g., Energy Efficiency, Delay, etc.) |

### 2.1. Incomplete Cooperative Game

As we mentioned earlier, energy efficiency of MAC protocol in WSN is very sensitive to number of nodes competing for the access channel. It will be very difficult for a MAC protocol to accurately estimate the different parameters like collision probability, transmission probability, and so forth, by detecting channel. Because dynamics of WSN keep on changing due to various reasons like mobility of nodes, joining of some new nodes, and dying out of some exhausted nodes. Also, estimating about the other neighboring nodes information is too complex, as every node takes a distributed approach to estimate the current state of networks. For all these reasons, an incomplete cooperative game could be a perfect candidate to optimize the performance of MAC protocol in sensor networks.

In incomplete cooperative game, the considered MAC protocol can be modeled as stochastic game, which starts when there is a data packet in the node's transmission buffer and ends when the data packet is transmitted successfully or discarded. This game consists of many time slots and each time slot represents a game slot. As every node can try to transmit an unsuccessful data packet for some predetermined limit (maximum retry limit), the game is finitely repeated rather than an infinitely repeated one. In each time slot, when the node is in active part, the node just not only tries to contend for the medium but also estimates the current game state based on history. After estimating the game state, the node adjust its own equilibrium condition by adjusting its available parameters under the given strategies (here it is contention parameters like transmitting probability, collision probability, etc.). Then all the nodes act simultaneously with their best evaluated strategies. In this game, we considered mainly three strategies available to nodes: transmitting, listening, and sleeping. And contention window size as the parameter to adjust its equilibrium strategy.

In this stochastic game, our main goal is to find an optimal equilibrium to maximize the network performance with minimum energy consumption. In general, with control theory we could achieve the best performance for an individual node rather than a whole network, and for this reason our game theoretic approach to the problem is justified.

Here, we define and as the transmission probability of the player 1 and player 2, respectively. Similarly, and represents the sleeping probability of player 1 and player 2 while is the conditional collision probability of player 2. As shown in Table 2, there are three strategies for both the players. First, player 1 transmits a packet with a probability , whose payoff is . Second strategy of player 1 is listening with a probability , whose payoff is Third strategy of player 1 is sleeping with a probability , whose payoff is . Finally, when both the players transmits simultaneously, their payoff are , and , respectively. Similarly, we can also calculate the probabilities of different strategies for player 2.

In addition, we can observe from the above equations that players can achieve their optimal response by helping each other to achieve their optimal utility. So the nodes have to play a cooperative game under the given constrained of energy. Here, the players can obtain the mixed strategy-based optimum response by adjusting their transmission probabilities to the variable game states. The value of the transmitting probability can be adjusted by tuning contention parameters, such as the minimum contention window ), the maximum contention window ( ), retry limit ( ), the maximum backoff stage ( ), arbitrary interface spaces (AIFS), and so forth. For simplicity, we choose contention window (i.e., properly estimating the number of competing nodes) as tuning parameter for adjusting transmission probability of a node.

### 2.2. Estimation of Competing Nodes

*N*) of competing nodes is the function of frame collision probability ( ) of a competing node. Also, the probability is constant and independent at each transmission attempt. A node transmits a data packet with the probability in a randomly chosen slot can be expressed as function of as in [14]

Now, by monitoring the channel all the nodes can independently measure the and , hence, can estimate the value of n as well. Equation (5) is the simple form of as for the simplicity we neglected the retry limit. The channel is an ideal and introducing no error to the reception of a packet other than collision. Also, capture effect is not considered.

This estimation mechanism gives good approximation but not the accurate results. There are some methods, especially [15, 16], to name a few, to accurately predict the number of competing nodes in the networks. In [17], authors presented batch and sequential Bayesian estimators to predict the number of competing nodes. In [15], authors presented two run time estimation methods named: "auto regressive moving average (ARMA)" and "Kalman Filters". These two methods are very accurate in predicting the number of competing nodes in saturation as well as in nonsaturation traffic conditions. However, all the methods presented in [15, 17] are too complex and heavy (in terms of energy consumption, etc.) to implement in sensor networks.

### 2.3. Motivation for Improved Backoff

As we mentioned earlier, estimating the game state accurately and timely are the key obstacles in formulating an incomplete cooperative game. Every node change its strategy by adjusting the contention window (i.e., properly estimating the number of competing nodes) and tries to achieve its optimal solution. However, according to [16] we cannot expect to find an algorithm that can give the theoretical optimum solution and runs in polynomial time, as the abovementioned problem has been proven to be NP-hard. So, if we allow each node to adjust its strategy after transmitting or discarding a packet rather than in each time slot we can relax the requirement on timeliness of the abovementioned game. Furthermore, we need a simple, light (in terms of energy and implementation) yet an effective suboptimal solution for the same. These challenges are the key motivation factors for us to introduce an improved backoff-based energy-efficient MAC protocol for WSNs, which can give a suboptimal solution to aforementioned incomplete cooperative MAC layer game.

### 2.4. Preliminaries

Number of nodes versus maximum throughput.

From the results presented in Figures 3, 4 and Table 3, we can observe that if we can adjust the size of the window or transmitting probability according to the number of competing nodes the maximum throughput can be achieved. This gives us an intuition to use Improved Backoff (IB) scheme for a suboptimal solution to incomplete cooperative game.

In this paper, we use a fixed size contention window, but a nonuniform, geometrically increasing probability distribution for picking a transmission slot (i.e., transmitting probability) in the contention window interval instead of traditional(here, traditional backoff procedure means CSMA/CA scheme with binary exponential backoff (BEB), unless and otherwise specified)backoff procedure. So, in this paper we present a suboptimal and a simple solution to achieve the optimum performance of a network.

## 3. Improved Backoff

In this section, we briefly introduce the improved backoff (IB), for more details on the same readers are refered to [14]. This is very simple scheme to integrate with any energy efficient MAC protocols for WSNs. This method does not require any complex or hard method to estimate the number of nodes. Furthermore, IB can easily accommodate the changing dynamics of WSNs.

### 3.1. IB Mechanism

Here, it is worth to note that IB scheme does not use timer suspension like in IEEE 802.11 to save energy and reduce latency in case of a collision. The only problem with the IB is fairness, however, for WSNs, fairness is not a problem due to two main reasons. First, overall network performance is more important rather than an individual node. Second, all nodes do not have data to send all the time (i.e., unsaturated traffic condition). Using IB may give us the optimum network performance as it reduces the collision to minimum.

### 3.2. Analytical Modeling of IB

The first equation in (10) indicates the backoff counter which is decremented if the channel is sensed idle. The second equation in (10) indicates the node defers the transmission of a new frame and enters stage 0 of the backoff procedure if it detects a successful transmission of its current frame or finds the channel busy or if it detects that a collision occurred to its current not successfully transmitted frame. The third equation in (10) indicates the node selects a backoff interval nonuniformly in the range of (1, CW) following an unsuccessful transmission. Rest of the equations shows the transition probabilities for two extra sates we added. Here, we take to introduce two extra states. The fourth equation in (10) represents the node waiting in the idle state for packet to arrive from the upper layer. The fifth equation in (10) shows the buffered packet enter to backoff procedure. The sixth and seventh equations in (10) represent the transition between buffer to idle state and back to buffer state according to availability of a packet, respectively. The last equation in (10) represents transition of backoff procedure to buffer state in case of a successful packet transmission.

### 3.3. Performance Evaluation

In this subsection we present, the performance comparison of incomplete cooperative game; that is, "Incomplete Game", our "considered" or "normal" MAC protocol, and IB-based MAC protocol in terms of channel efficiency, medium access delay, and energy-efficiency. The latter two protocols are the same in nature except for their backoff procedure. Here, we fixed the channel rate to 1 Mbps with an ideal channel condition. For the "normal" MAC protocol maximum retry limit is set to 6 ( ), minimum contention window is set to 16 (also for the IB Based MAC), and traffic model is set to nonsaturation. The backoff algorithm (BA) performed in a time-slotted fashion. A node attempts to attain the access the channel only at the beginning of a slot. Furthermore, all nodes are well synchronized in time slots and propagation delay is negligible compared to the length of an idle slot. For the performance evaluation, we carried out simulation in Matlab.

Here, we define network load in terms of the number of nodes that are contending for the access medium. Another approach is to consider total arrival packet rate to the network as an offered load. The main parameters for our simulation are based on [18] and listed in Table 4. For calculating the energy consumption in nodes, we choose ratio of idle: listen: transmit as 1 : 1 : 1.5, as measured in [19]. For the simulation results we do not consider the technology adopted at the Physical layer, however the physical layer determines some network parameter values like interframe spaces. Whenever necessary, we choose the values of the physical layer dependent parameters by referring to [18]. In case of "Incomplete Game", we assume that each node estimates the game state timely and accurately by detecting the channel. The results obtained here are the average values of our collected data.

From Figure 9, we can see that as number of nodes increases NM scheme waste more energy due to increase in collision and retransmission attempts. In contrast, IBM wastes very less energy due to its unique characteristics of collision avoidance. Similarly, "Incomplete Game" can also give the comparative performance to IBM, as it also reduces collision by adjusting its equilibrium strategy. Here it is worth to note that during the "Incomplete Game" all the nodes will switch to sleep mode when there is no communication. From all aforementioned results, we can see the superiority of IBM over NM. Accepting IBM as backoff scheme can increase the overall performance of an energy efficient MAC protocol to a large extends and we can also get the suboptimal solution for an incomplete cooperative game.

### 3.4. Applicability and Extendibility of the Incomplete Game

In this paper, we use the concept of incomplete cooperative game to improve the performance of a WSN MAC protocol. Using the presented method here we can formulate a game for dynamic duty cycle adjustment in wireless sensor networks. With a proper fairness mechanism, it is also possible to extend our scheme to general wireless networks (i.e., IEEE 802.11). Furthermore, it is possible to extend our scheme to answer the selfish behavior of a node in IB and erroneous channel conditions as well.

## 4. Conclusions

In this paper, we used the concept of incomplete cooperative game to model the WSN MAC protocol for energy-efficient design. Moreover, we introduced IB for an energy-efficient MAC protocol in WSNs. It is very easy to implement in WSNs and also we do not need any complex estimation algorithm to calculate the number of nodes in the network. From the results, it is clear that IB can provide a suboptimal solution to an incomplete cooperative game.

## Declarations

### Acknowledgments

The authors would like to express their sincere thanks to the anonymous reviewers for their insightful comments that helped in improving the quality and presentation of this paper. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2010-0018116).

## Authors’ Affiliations

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