Abstract
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The connectivity is one of the key issues that requires significant study, since few network services can function properly if the network is disconnected. Specially, the network topology is rapidly changed due to high mobility in vehicular ad-hoc networks (VANETs). Therefore, it is crucial to accou...

The connectivity is one of the key issues that requires significant study, since few network services can function properly if the network is disconnected. Specially, the network topology is rapidly changed due to high mobility in vehicular ad-hoc networks (VANETs). Therefore, it is crucial to account for accurate distributions of vehicles on the road [1, 2]. In this thesis, we study the statistical properties of network size in a so-called Markov population highway. We derive the exact probability of network size and discuss the effect of population process rates on the number of vehicles. Moreover, in general the vehicle velocity is modeled as a Gaussian distribution and the vehicle arrival time is seen as the exponential distribution with the fixed rate [2]. In this thesis, we improve the mobility model using the Brownian motion with the rate of arrival time between two consecutive vehicles. We then derive the probability distribution for the random locations of vehicles in terms of time t and arrival rate. In this thesis, we investigate the statistical properties of network size in vehicular ad-hoc networks. The vehicles arrive or depart at the highway through one of the traffic entry points according to a Markov population process. Using the general immigration-death process-coined as general arrival rate and general departure rate, we derive the probability distribution of network size (the number of vehicles in a segment). Another work, we propose a new mobility model for the movement of vehicles in VANETs. Using the theory of Brownian motion and renewal process, we develop the statistical model for random locations of vehicles.

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