# Multi-Agent Modeling and Jamming-Aware Routing Protocols for Movable-Jammer-Affected WSNs
## 1 Introduction  
Wireless sensor networks (WSNs) are networks of sensor devices that can monitor and record physical or environmental conditions, such as temperature, humidity, sound, etc., and communicate wirelessly with a central location [1]. WSNs have many applications and benefits, such as data center management [2], environmental monitoring [3], health care [4, 5], smart homes [6, 7], smart military [8], etc. It is evident that many of these application scenarios are safety-critical or mission-critical, where the failure of a sensor node or the corruption of data can lead to significant consequences, such as damage to the environment, loss of assets, or even loss of human lives. Therefore, ensuring the reliability of WSNs is of utmost importance. However, WSNs frequently encounter numerous security challenges and vulnerabilities as a result of their low level of security, limited resources, shared medium, and dynamic topology [9], and these threats naturally reduce the reliability of WSNs. Jamming attacks are among these vulnerabilities. Jamming is a form of denial-of-service attack that disrupts wireless communication between sensor nodes by emitting noise or signals that the same frequency band [10]. This type of attack can reduce network performance, decrease throughput, increase energy consumption, disrupt routing protocols, and so on [10]. Several techniques have been proposed to prevent or mitigate jamming attacks on WSNs, such as encryption schemes [10], intrusion detection systems [10, 11], agent-based models [12, 13], and evolutionary game theory [14, 15]. Additionally, an interesting fact we have noticed is the lack of research on movable jammers, as also highlighted in severalsurveys on jammers [16; 17]. This refers to situations where the position of a jammer device can change over time. In reality, for war or malicious damage scenarios, movable jammers pose a significant problem and can amplify the destructive power of attacks, while also making it challenging for defenders to detect and counter their presence. Furthermore, it is imperative to investigate the design of a corresponding defensive confrontation mechanism to counter the threat of a mobile jammer. To model the reliability of WSNs, several approaches have been proposed in the literature. These approaches include statistical models, probabilistic models, and simulation-based models. These models aim to capture the various factors that affect the reliability of WSNs, including the sensor node characteristics, network topology, and communication protocols. Considering the ad hoc network characteristics of sensor nodes in WSNs and the mobility of jammer devices, the multi-agent modeling method is a suitable approach for reliability modeling. Therefore, to analyze the impact of movable jammers on the reliability and performance of WSNs, this paper proposes a multi-agent approach that includes various agents such as sensor nodes, base stations, and jammers. The jammers utilize constant jamming, are mobile, and have various configurations. Additionally, the study develops a jamming-aware routing protocol, called JRP, to enhance the resilience of WSNs against jamming. JRP utilizes two independent factors, depth and jamming. The jamming ensures that the constructed routing path avoids the jammer's affected area, while the depth guarantees that the sensor node selects the next information relay node that is closer to the base station. The final route construction considers the weightage of these two factors. The main contributions of this research include:  
1. Investigation of movable jammers: Our study is pioneering in its investigation of movable jammers as no previous research has explored this area. We present the first investigation of the impact of movable jammers on WSN reliability and performance utilizing a multi-agent approach. 2.