In wireless sensor networks (WSNs), each node controls its sleep to reduce energy consumption without sacrificing message latency. In this paper we apply the game theory, which is a powerful tool that explains how each individual acts for his or her own economic benefit, to analyze the optimal sleep schedule for sensor nodes. We redefine this sleep control game as a modified version of the Prisoner’s Dilemma. In the sleep control game, each node decides whether or not it wakes up for the cycle. Payoff functions of the sleep control game consider the expected traffic volume, network conditions, and the expected packet delay. According to the payoff function, each node selects the best wake-up strategy that may minimize the energy consumption and maintain the latency performance. To investigate the performance of our algorithm, we apply the sleep control game to X-MAC, which is one of the recent WSN MAC protocols. Our detailed packet level simulations confirm that the proposed algorithm can effectively reduce the energy consumption by removing unnecessary wake-up operations without loss of the latency performance.
To reduce the energy consumption, each sensor node employs duty cycling where each node periodically sleeps [
In this paper, we mathematically model and analyze the duty cycling of nodes to improve the energy efficiency of a MAC protocol without sacrificing the message latency. The communication activity of nodes is similar to human economic activities since both activities aim to maximize benefits—network performance for nodes versus economic profit for human—without global information for the entire network or market. In this regard, we adopt the game theory, which is a powerful tool that explains how each individual acts for his or her own economic benefit, as a tool for modeling and analyzing the duty cycle operation of sensor nodes. Since the communication activity of each node prioritizes over communication activities of other nodes and each node operates independently, the communication activity of a node can be regarded as the noncooperative game [
In the sleep control game, each node decides whether or not it wakes up for the cycle. Therefore, each node selects its strategy based on the payoff function. And, the wake-up probability is the key for each node’s strategy in the sleep control game. Since the sleep state of a node affects both the energy consumption and the message latency, the wake-up probability of each node needs to consider the expected traffic volume, network conditions, and the expected packet delay, which are three components for the payoff function in the sleep control game. According to the payoff function, each node selects the best wake-up strategy which may minimize the energy consumption and maintain the latency performance. We show that the sleep control game is stable and it has Nash Equilibrium with the designed payoff function.
To investigate the performance of our algorithm, we apply the sleep control game to X-MAC [
A game theory describes and analyzes decision making process. In this paper, we limit our discussion to noncooperative model: the interaction between rational decision makers. The term rational decision makers here refer to those who are selfish and act for their best interest. The model described above is referred to as a “game,” and the decision makers are called “players.” This situation could be seen as follows: players choose a strategy from predefined list of strategies that will maximize their profit. A utility function would be deployed by each player to analyze another player’s strategy selection. A normal form of a game
From the outcome of this model, we can conclude that stable states exist in the model. We figure these states are the Nash Equilibria. A system would be in Nash Equilibria when any individual player cannot increase profit by choosing any other strategies. In other words, Nash Equilibria could be expressed as the consistent projection of the outcomes of which there would be no incentive for each individual player to choose different strategies to maximize its profit.
However, although Nash Equilibria do exist in the model, Nash Equilibria do not mean the best outcome of a game. In many cases, Pareto optimality [
For all strategies
There have been a few studies that apply game theory to MAC protocol design [
In WSNs, quite a few studies applied the game theory to the routing protocols [
Researches in earlier stage of duty cycling [
To our knowledge, AMAC [
A few more recent schemes [
While previous works [
To exploit a heuristic sleep control, the schemes discussed so far require a predefined trigger condition such as traffic occurrence [
Consider that each node has a set of
We model the interaction among wireless sensor nodes as a noncooperative game since each node operates independently and prioritizes its communication over neighbor’s communications. Since each node is selfish and blind to the neighbor’s strategies, the interaction model is similar to the Prisoner’s Dilemma. We call the model as sleep control game.
We define the sleep control game by using the expected message latency, node’s wake-up probability, contention measure, and the expected traffic volume. In practice, it is hard for a wireless sensor node to learn directly the wake-up probabilities of neighbors. Each node infers the neighbor’s wake-up probabilities by observing the network condition of the previous cycle. In addition, it is hard to predict an end-to-end packet delay from a source to a destination. However, each node can estimate the packet delay by itself. The expected message latency can be estimated by using the wake-up probability, contention measure, and the expected traffic volume.
We assume that each node dynamically adjusts wake-up probability,
We assume that (
If
We define the utility function of each node
Since
A sleep control game
The latency affection factor,
The payoff function can be interpreted as the gain of utility from the packet latency discounted by the wake-up cost. One property of this game is that the computation of the payoff function does not require the explicit exchange of wake-up probability of each node among the nodes. Thus, this game can be played and implemented in a distributed manner. In addition, this game reduces the energy consumption and the bandwidth usage for transmitting control messages.
Since the strategy
In WSNs, the packet latency is influenced by node’s buffer state, traffic volume, and the wake-up state of a receiver node. When a node
The sleep delay,
Equation (
By using (
According to (
The wake-up probability needs to be stable and unique in order to find the best strategy. To verify the stability of wake-up probability, we should analyze the equilibrium of the sleep control game and show that the equilibrium is unique. By proving the following three theorems, we will show the existence (Theorem
We denote the strategy (wake-up probability) selection for node
The utility function
Under Assumption
Assumption
Since payoff function
Define a function
Let
Under Assumptions
The Hessian of function
By second-order conditions [
The equilibrium condition (
We call a Nash Equilibrium a nontrivial equilibrium
Note that (
If the control game
Suppose that there are two nontrivial Nash Equilibriums
Since
Each node
A Nash Equilibrium
For a system of homogeneous users, suppose Assumption
In this section we analyze the performance of our algorithm by applying the sleep control game to X-MAC [
Simulation parameters.
Parameters | |
---|---|
Topology of a network | 400 random nodes |
Simulation time | 1 hour |
Data packet size | 100 bytes |
Number of packets for an event | 10 packets |
Basic cycle time of X-MAC, 4 |
300 ms (5% duty cycle) |
Event rate | 0.1% per |
Power consumption (Tx, Rx, idle) | 30 mW, 15 mW, 15 mW |
Latency affection factor, |
1 |
Maximum distance from a sink node | 10 hops |
Figure
The wake-up probability according to time elapse.
According to the results, a node with
Note that a node with
Figure
The network throughput according to time elapse.
Figure
The average message latency according to hop counts.
Figure
The distribution of the packet latency for a single hop communication.
Like X-MAC,
When a source generates multiple messages, the latencies of the following messages can be reduced since nodes on the common routing path already wake up after reporting the first message. Therefore,
According to the results of Figures
Figure
The average energy consumption according to time elapse.
When there is no traffic,
Figure
The average message latency according to the latency affection factor,
Figure
The average energy consumption according to the latency affection factor,
As shown in Figures
Energy-delay product according to the latency affection factor.
In this paper, we introduce a novel game theoretic MAC approach to improve the energy efficiency of WSNs. Our scheme adjusts nodes’ wake-up schedules dynamically by exploiting the wake-up probability based on the game theory, which is an efficient tool for analyzing the interaction between multiple independent rational players. To model the interaction between sensor nodes, we redefine a sleep control game as a modified version of the Prisoner’s Dilemma. Payoff function of the sleep control game considers the expected traffic volume, network condition, and the expected message latency.
The major contribution of this paper is that it introduces a mathematical approach to control the duty cycle of a sensor node while the conventional researches exploit a heuristic approach. With the detailed packet level simulations, we confirm that the sleep control game can effectively reduce energy consumption without sacrificing the network performance. Furthermore, the sleep control game can effectively deal with burst traffic and it is also suitable for massive sensor network with inexpensive sensor nodes.
The authors declare that they have no competing interests.
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government (MSIP) (no. NRF-2015R1A2A1A16074932). This research was also supported by the MSIP (Ministry of Science, ICT and Future Planning), Korea, under the ITRC (Information Technology Research Center) support program (IITP-2015-R0992-15-1012) supervised by the IITP (Institute for Information & Communications Technology Promotion).