Point processes on the real line have many useful applications, both when describing events in time, or the distributions of points along a line in space. In this report a class of point processes named Markov Arrival Processes are dened, described and used for baysian inference upon tree sets of data. The data upon witch the inference is made, come from the FleetFet project at the University of Mannheim. This data contains the placement of cars on a freeway, and it is the aim of the report to introduce models that can be used to describe these as point processes on the real line. The rst to chapters give a basic presentation of the baysian approach to inference and point processes on the real line. The third chapter describes the Markov Arrival processes and some of its properties. Thereafter several summary statistics are dened and some results fore these are obtained. The sixth chapter describe the data and the Metropolis-Hastings algorithm. The last two chapters describe two direct models used to describe the data as point processes, the poisson process and the Markov modulated renewal process. The distributions of the parameters of these models are calculated, and the abilites of the models to describe the data is assessed. The appendixes contain various results for markov chains used in the report, as well as several functions in R.