Vehicle ad hoc networks (VANETs) have become a popular topic in modern research. The main advantages of these networks include: improved security, traffic optimization, and infotainment. However, deploying such networks in practice requires extensive infrastructure. To estimate the network load, one needs to have information about the network, such as the number of clusters, cluster size, etc. Since VANETs are formed by vehicles that rapidly change their location, the network topology is constantly changing, making its analysis by deterministic methods impossible. Therefore, in this dissertation, we use probability theory methods to obtain probability distributions of such fundamental network properties, such as the number of clusters, cluster size, and the number of disconnected vehicles in the case in which the vehicles are located on a highway. In previous articles, some of these characteristics are obtained only in terms of average values, while the total distributions remained unknown. The distribution of the largest cluster size is an important characteristic of the network. It is derived in the dissertation for the first time. We also study the distribution of the number of clusters and the size of the average cluster in the case of a 2D map with an almost arbitrary road topology. To the best of our knowledge, these results are the first for such a general map case.
Studying these properties raises a number of new questions about how these network properties change over time. We obtain distributions of the network characteristics, such as the duration of communication between vehicles, and the duration of cluster existence. We also derive the probability that a cluster exists between two time moments, as well as other network properties. The obtained distributions are new in the case of the Markov channel model. The results regarding the distribution of cluster lifetime and the probability of cluster existence between two fixed time moments are obtained in the literature for the first time.
This dissertation also addresses the security aspect of VANET. We consider single and multichannel anti-jamming games in the case in which two communicating vehicles are being pursued by the jammer, which tries to disrupt the communication. The optimal strategies of the vehicles and the jammer are described as the Nash equilibrium of this game. We prove theorems that express Nash equilibrium through communication parameters. The considered model with quadratic power term is new as well as the results regarding the Nash equilibrium in the single and multichannel cases. We also first examine performance of such state-of-the-art machine learning algorithms as Dueling Q-learning and Double Q-learning, which by trial and error, successfully converge to the Nash equilibrium, deduced theoretically
