k -barrier coverage reliability evaluation for wireless sensor networks using two-dimensional k -within-consecutive- r  ×  s -out-of- m  ×  n:F system

The reliability of k-barrier coverage for wireless sensor networks is evaluated in this article. We construct a two-dimensional k-within-consecutive-r × s-out-of-m × n:F system to describe the k-barrier coverage problem and propose the definition of the k-barrier coverage reliability. If the sensing radius r of each sensor is equal to half of the horizontal distance d between two adjacent sensors, then the formula for calculating the k-barrier coverage reliability can be derived directly. If r is a positive integer multiple of d, then a recursive algorithm is applied to calculate the coverage reliability. The effects of the probability that sensors are active, the number of rows of deployed sensors and the number of sensors in each row on the coverage reliability are also analyzed using some illustrative examples. The results show that, if r = d/2, the reliability of a barrier decreases with an increase in the length of the barrier; if r = t × d (t is a positive integer), the reliability of a barrier hardly decreases with an increase in the length of the barrier.