# Reliability Evaluation for Clustered WSNs under Malware Propagation
## 1 Introduction
Even if the time to propagate malware may be randomly distributed, the decision to propagate is not. To solve this problem, we are motivated to leverage a strategic game to obtain the malware's expected propagation probability. Game theory investigating strategic decision-making among players has been widely employed in the field of WSN security [4; 5; 6; 7; 8; 9; 10; 11; 12] such as optimizing intrusion detection strategies [5; 6; 10; 11; 12], securing data aggregation [7], localizing malicious nodes [8], and providing secure defenses for virtual sensor services [9]. This efficient mathematical tool is also suitable to explore different critical decisions during malware propagation. Usually, WSNs guard susceptible sensor nodes from malware attacks using Intrusion Detection Systems (IDSes). However, this method inevitably increases nodes' costs upon launching IDS agents, since sensor nodes have limited computational resources. Malware achieves greater gains by infecting more sensor nodes and eavesdropping on sensed data from infectious nodes, but this infection behavior obviously increases the probability of detection by IDSes. Thus, malware selects an optimal infection strategy to determine its propagation. In this paper, we study reliability evaluation for clustered WSNs under epidemic-malware propagation. We use a strategic game to predict malware's infection behavior whose consequences we integrate into the transition probability upon infection of a sensor node. As a result, we determine how to relate the intent of malware infection to the CTMC's randomness. Next, we propose a novel measure to reflect the reliability of a sensor node. After considering clustered WSNs as parallel-serial-parallel systems due to their communication modes, we obtain equations to compute the reliability of a cluster, a route, and a clustered WSN, respectively. Our main contributions are as follows:  
1. We relate the intent of malware infection to the CTMC's randomness by introducing a strategic game that can predict malware's infection behavior. In this manner, state transitions of a sensor node that arise from malware actions can be modeled by the CTMC; and
2. We propose a novel measure to compute the Mean Time to Failure (MTTF) of a sensor node, which represents the reliability of a sensor node continuously performing tasks such as sensing, transmitting, and fusing data. Thus, we can deduce the reliability of a cluster, a route, and a clustered WSN from the perspective of a parallel-serial-parallel system, respectively. This method of reliability evaluation for clustered WSNs under epidemic-malware propagation can help establish theoretical foundations that guide rules for applying reliability techniques. Consequently, WSNs that guarantee reliable delivery of sensor nodes' sensed data may be realized. The rest of this article is organized as follows: we first review related work and highlight the salient features of our approach in Section 2. We describe infections as state transitions from the view of a CTMC in Section 3. We obtain the infection probability by introducing a strategic malware-infection game in Section 4. We propose measures of reliability evaluation for clustered WSNs under the scenario of epidemic-malware propagation in Section 5. We validate the proposed measures' efficacy in Section 6. Finally, we conclude the article in Section 7.