Modelling co-operative MAC layer misbehaviour in IEEE 802.11 ad hoc networks with heterogeneous loads

Misbehaviour due to back-off distribution manipulation has been one of the significant problems faced in IEEE 802.11 wireless ad hoc networks which has been explored recently by the research community. In addition, collusion between misbehaving nodes adds another dimension to this security problem. We examine this problem in a three-node network scenario wherein two nodes are assumed to be malicious colluding adversaries causing unfair channel access to the other legitimate node. The misbehaving nodes, through back-off manipulation, will try to minimize the channel access share got by the legitimate node and at the same time maximize the detection delay to detect such an attack. We explore this problem and its solution, analytically, in a non-saturated setting, by modelling a single IEEE 802.11 node as a discrete time Markov chain (DTMC) and suggest a measure for evaluating fairness in the network. We then propose an attacker-detector non-linear optimization model through which the joint optimal attacker distribution is evaluated by applying results from the area of variational calculus. We finally use the sequential probability ratio test (SPRT) for estimating the average number of samples for detecting colluding adversaries in the network. We validate all the models using MATLAB and verify the model results by sampling values from the evaluated optimal attacker distribution using a robust statistical library called UNU.RAN.