On Detection of Critical Events in a Finite Forest using Randomly Deployed Wireless Sensors

Ecosystem of a forest suffers from many adverse events such as wild-fire which can occur randomly anywhere in the forest and grows in size with time. This paper aims to analyze performance of a network of randomly deployed wireless sensors for the early detection of these time-critical and time-evolving events in a forest. We consider that the forest lies in a confined space (e.g. a circular region) and the wireless sensors, with fixed sensing range, are deployed within the boundary of forest itself. The sensing area of the network is modeled as a finite Boolean-Poisson model. In this model, the locations of sensors are modeled as a finite homogeneous Poisson Point Process (PPP) and the sensing area of each sensor is assumed to be a finite set. This paper aims to answer questions about the proximity of a typical sensor from a randomly occurred event and the total sensing area covered by sensors. We first derive the distribution of contact distance of a FHPPP and the expression of the capacity functional of a finite Boolean-Poisson model. Using these, we then derive the probability of sensing the event at time t, termed event-sensing probability.