The use of wireless sensor networks (WSNs) based surveillance applications to detect intruders requires accurate methods for monitoring, tracking the trajectories of intruders, and energy consumption of sensors. In this paper, we propose a model to formally define the monitoring WSN lifetime based on the intruder's behavior. We address the problem of designing and analyzing of the crossing strategies of the border crossings with a priori knowledge of their arrival rate using WSN. We focus on two crossing strategies; namely, the orthogonal and progressive crossing strategy. Given a monitored area considered as the union of multi-thick lines architecture, we propose a deployment scheme of sensors to ensure good detection for both strategies and present a method to compute and compare their network lifetime upon. Some numerical simulation results are collected to analyze the related performance.