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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

The obstacle avoidance problem in geographic forwarding is an important issue for location-based routing in wireless sensor networks. The presence of an obstacle leads to several geographic routing problems such as excessive energy consumption and data congestion. Obstacles are hard to avoid in realistic environments. To bypass obstacles, most routing protocols tend to forward packets along the obstacle boundaries. This leads to a situation where the nodes at the boundaries exhaust their energy rapidly and the obstacle area is diffused. In this paper, we introduce a novel routing algorithm to solve the obstacle problem in wireless sensor networks based on a game-theory model. Our algorithm forms a concave region that cannot forward packets to achieve the aim of improving the transmission success rate and decreasing packet transmission delays. We consider the residual energy, out-degree and forwarding angle to determine the forwarding probability and payoff function of forwarding candidates. This achieves the aim of load balance and reduces network energy consumption. Simulation results show that based on the average delivery delay, energy consumption and packet delivery ratio performances our protocol is superior to other traditional schemes.

Wireless sensor networks (WSNs) are composed of many tiny devices, each with sensing and data storing, processing and communication capabilities. Sensor networks have many potential applications, such as battlefield surveillance, environmental monitoring and industrial asset management. However, the design of energy efficient, scalable routing algorithms remains a challenging issue for researchers.

Recently, some research efforts have focused on establishing efficient routing paths for transmitting packets from a sensor node to a sink in wireless sensor networks [

Existing obstacle handling techniques mainly use the following two approaches to solve the problem: the right hand rule [

In this paper, we propose a novel protocol to handle the obstacle problem based on forwarding mechanisms in sensor networks. Our protocol first computes the connectivity degree set for every node and separates the degree set into out-degree and in-degree sets. Given that some nodes may have zero out-degree, we establish a concave region in the sensor network. Packets cannot be forwarded to the concave region and this approach can avoid lost packets and reduce the transmission delay. Secondly, during the phase of forwarding node selection of source nodes, the source node considers residual energy, out-degree and forwarding angle of forwarding candidates and infers the forwarding probability according to these three factors. Furthermore, we provide a game theory model based on the forwarding probability of forwarding participants and prove that in the game model a Nash equilibrium exists.

The rest of this paper is organized as follows: Section 2 presents related works on obstacle based routing and game theory-based protocols in wireless sensor networks. Section 3 presents the network initialization and how to form the concave region. In Section 4, we present the game theory model and prove that a Nash equilibrium exists in the game model introduced. Finally, we perform simulations to evaluate the performance and conclude this paper in Sections 5 and 6.

To the best of our knowledge, this paper is the first to present the obstacle avoidance routing issue for wireless sensor networks from a game-theory perspective. Therefore, we summarize the obstacle avoidance routing and game theory based routing literature.

Obstacle-avoidance routing algorithms in wireless sensor networks have been widely studied [

Geometric obstacle avoidance is proposed in [

The cost based approach [

Hybrid techniques use at least two obstacle avoidance techniques. The motivation is the improved efficiency of the path and the guaranteed delivery of the message, and they are used when only one of the two techniques is not enough to achieve these requirements. The disadvantage is the increased overall complexity. In [

Game theory has been used in the past as a model to study different aspects of computer and communication networks. Recently, more and more researchers have focused on developing wireless network algorithms using game theory. The most important application of game theory to wireless sensor networks is routing algorithm design. In [

In the incentive mechanism of wireless networks routing protocols,

In our work, since the nodes are static, all nodes know their own locations before network initialization. In the initialization stage of the network, each node sends its own location information to its one hop neighbors. Meanwhile, each node also receives all the location information from all its one hop neighbors. When nodes acquire their neighbor location information, they compute the distance between themselves and the sink, and the distance between every one hop neighbor and the sink. Then, each node compares those distances and concludes which node is closer than itself to the sink, then it counts the number of one hop neighbors closer to the sink in Euclidean distance between nodes, and this number is its out-degree number. These nodes are then included in the out-degree set. The rest of the nodes that are not in the out-degree set constitute the in-degree set. Obviously, nodes in the in-degree set are farther away from the sink. After the computation and comparison are finished, each node has acquired out-degree and in-degree sets of their own. There are two extreme cases that could happen for the out-degree set or the in-degree sets of some nodes.

The in-degree of some node is zero. From

The out-degree of some node is zero. In

The existence of a zero out-degree node can have a fatal influence on the routing of wireless sensor networks. Thus, we present a separate discussion of these nodes. From

In this paper, when a source node

Forwarding candidate nodes would take the following three factors into consideration to form their forwarding probabilities:

The ratio composed by the out-degree of their own and the average out-degree for all nodes. We denote it as _{i}/O_{a}_{i}_{a}

The ratio composed by current energy and initial energy (_{{current}}/E_{{initial}}_{i(ci)}

The cosine value of the angle composed by the line linked candidate node

For any candidate node _{i(ci)}_{i}/O_{a}

∠

_{SD}_{SD}_{SD}_{SD}_{SD}_{SD}

In the two equations above, _{elec}_{fs}_{i}_{SD}_{SD}_{SD}_{SD}_{SD}_{SD}_{SD}_{SD}_{SD}_{SD}_{SD}_{SD}_{SD}_{SD}_{SD}_{SD}_{SD}_{SD}

For any node

We define that for each forwarding process in one game, the forwarding participants of the source node are in the out-degree set. The strategy space of participants is _{i}_{i}

During the game progress, different strategies lead to different benefits for each participant. The benefit to participants is described by the payoff function. For any participant, the benefit has some relation with strategy. We assume the strategy combination is _{i}_{i}_{i}

In the game period, each participant would like to use its optimal strategy to maximize its payoff. Therefore, the benefit and cost of the participant would impact the strategy for all the nodes located on the routing path. Furthermore, it would impact the transmission reliability grade of the routing path. We consider the transmission reliability grade as the benefit of intermediate nodes. We assume for strategy combination _{up}_{ij}_{j}_{i}_{i}_{i}_{j}

In this section, we make a simulation to evaluate the performance of obstacle modeling. Firstly, we introduce the performance metrics and the simulation scenarios. Then we evaluate the system performance with the given scenarios and parameters. Finally, we show the performance comparisons between our algorithm and SPEED [

We use three metrics to evaluate the performance. The average delivery delay, energy consumption and packet delivery ratio. The size of the sensor network is set to 200 m × 200 m where 100 nodes are uniformly distributed. An obstacle is created at the center of the area;

At the aspect of packet delivery ratio, from

In this section, we compare SPEED, GPSR and our algorithm under different obstacle area conditions on the following aspects: average delivery delay, energy consumption and packet delivery ratio. There are 100 nodes in the sensor field and the transmission rate is 50 packets per second. The initial area of the obstacle for the whole sensor field is 5% and it finally increases to 50% and the shape of the obstacle does not change. For the instance where the obstacle is expanding, the transmission rate and the number of nodes are constant. Moreover, the area of the sensor field is constant. It means that, the density of nodes is becoming higher per unit time. Therefore, we only need expand the area of the obstacle in the sensing field, we can compare two aspects of performance: expanding obstacle and higher density. Concerning SPEED, GPSR and our algorithm, when the area of the obstacle is changed, the performance of delivery delay, energy consumption on the boundary and the packet delivery ratio would have a significant influence. In the following, we will introduce the performance comparison with changing obstacle area.

In

In

We next compare algorithms under the condition of expanding obstacle with packet delivery ratio in

In this paper, we introduce a game theory-based obstacle avoidance scheme. In the process of network initialization, we use the connectivity property of nodes to determine the concave region that cannot forward any packets. This approach improves the transmission success rate and decreases the transmission delays of packets. In the aspect of setting up the routing path, we consider the residual energy, out-degree and forwarding angle of forwarding candidates. We conclude the forwarding probability and payoff function of forwarding participants. Finally, we prove the existence of s Nash equilibrium for the proposed game model. In our future, we plan to implement our algorithm in s real application scenario to verify the effectiveness in the real world. Also, in this paper, we assume that all nodes are stationary. There are some application scenarios where we need the nodes to be able to move. In such a case, we will need to consider the nodes’ mobility in our future work.

Illustration for the node out-degree is zero and in-degree is zero cases in sensor networks with obstacles.

Construction of a forbidden region for a concave region.

Illustration for forwarding angle with source, destination and forwarding candidate node.

Illustration for different routing path according to minimum angle and shortest path.

Average delivery delay with different transmission rates.

Energy consumption with different transmission rates.

Packet delivery ratio with different transmission rates.

Average delivery delay with expanding obstacle area.

Energy consumption with expanding obstacle area.

Packet delivery ratio with expanding obstacle area.