Formal Probabilistic Analysis of a Wireless Sensor Network for Forest Fire Detection

Abstract

Wireless Sensor Networks (WSNs) have been widely explored for forest fire detection, which is considered a fatal threat throughout the world. Energy conservation of sensor nodes is one of the biggest challenges in this context and random scheduling is frequently applied to overcome that. The performance analysis of these random scheduling approaches is traditionally done by paper-and-pencil proof methods or simulation. These traditional techniques cannot ascertain 100% accuracy, and thus are not suitable for analyzing a safety-critical application like forest fire detection using WSNs. In this paper, we propose to overcome this limitation by applying formal probabilistic analysis using theorem proving to verify scheduling performance of a real-world WSN for forest fire detection using a k-set randomized algorithm as an energy saving mechanism. In particular, we formally verify the expected values of coverage intensity, the upper bound on the total number of disjoint subsets, for a given coverage intensity, and the lower bound on the total number of nodes.

Formal probabilistic performance verification of randomly-scheduled wireless sensor networks

“…The analysis, presented in this paper, primarily illustrates the effectiveness of the existing higher-order-logic developments for the other performance metrics. Indeed, the lifetime verification has been possible thanks to the sound and complete formalizations of the network coverage, done in (Elleuch et al, 2011(Elleuch et al, , 2013a, along with the detection probability and delay, presented in (Elleuch et al, 2015). Hence, it would not have been possible to effectively achieve the main lifetime proof if, for example, there was a missing assumption on one of the design parameters in the detection part.…”

“…The set S Cn can be simply deduced as non-empty. Similarly, as the network coverage is decreasing versus the parameter k (Elleuch et al, 2013a), the best coverage is then achieved for (k = 1). We hence target a good QoS value for coverage, but which can not exceed C n (1).…”

“…The formal analysis of the optimal lifetime problem required many intermediate results in relation with the behavior of the three performance attributes, which are the detection delay, the detection probability and the network coverage. A brief summary of the required lemmas is provided in Table 2 (Elleuch et al, 2013a(Elleuch et al, , 2015, and the interested reader can access them from (Elleuch, 2013).…”