Security for Multihop Wireless Networks

Fighting against Black Hole Attacks in Mobile Ad Hoc Networks  ◾  93

4.6.2 Model for the Detection of Black Hole Nodes

is model takes into account the effect of false negatives. False positives do not

affect the detection time of black hole nodes, so p

fp

is not introduced in this model.

e effect of false positives will be studied later.

Using λ we can model the network using a 2D continuous time Markov chain

(2D-CTMC) with states (c

p

, c

n

), where c

p

represents the number of collaborative

nodes that have a positive about the black hole node at time t, and c

n

represents

the number of collaborative nodes that have a negative of the black hole node (note

that, in this case, is a false negative). At the beginning all nodes have no informa-

tion about ...