$$(alpha , tau )$$-Monitoring for event detection in wireless sensor networks |
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| Authors: | Ran Bi Jianzhong Li Hong Gao Yingshu Li |
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| Affiliation: | 1.School of Computer Science and Technology,Harbin Institute of Technology,Harbin,China;2.Department of Computer Science,Georgia State University,Atlanta,USA |
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| Abstract: | Detecting abnormal events is one of the fundamental issues in wireless sensor networks (WSNs). In this paper, we investigate ((alpha ,tau ))-monitoring in WSNs. For a given monitored threshold (alpha ), we prove that (i) the tight upper bound of (Pr [{S(t)} ge alpha ]) is (Oleft( {exp left{ { - nell left( {frac{alpha }{{nsup}},frac{{mu (t)}}{{nsup}}} right) } right} } right) ), if (mu (t) < alpha ); and (ii) the tight upper bound of (Pr [{S(t)} le alpha ]) is (Oleft( {exp left{ { - nell left( {frac{alpha }{{nsup}},frac{{mu (t)}}{{nsup}}} right) } right} } right) ), if (mu (t) > alpha ), where (Pr [X]) is the probability of random event (X,, S(t)) is the sum of the monitored area at time (t,, n) is the number of the sensor nodes, (sup) is the upper bound of sensed data, ( mu (t)) is the expectation of (S(t)), and (ell ({x_1},{x_2}) = {x_1}ln left( {frac{{{x_1}}}{{{x_2}}}} right) + (1 - {x_1})ln left( {frac{{1 - {x_1}}}{{1 - {x_2}}}} right) ). An instant ((alpha ,tau ))-monitoring scheme is then developed based on the upper bound. Moreover, approximate continuous ((alpha , tau ))-monitoring is investigated. We prove that the probability of false negative alarm is (delta ), if the sample size is Open image in new window Open image in new window Open image in new window | |
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