  Many studies suggest that searching for parking is associated with
significant direct and indirect costs. Therefore, it is appealing to reduce the
time which car drivers spend on finding an available parking lot, especially in
urban areas where the space for all road users is limited. The prediction of
on-street parking lot occupancy can provide drivers a guidance where clear
parking lots are likely to be found. This field of research has gained more and
more attention in the last decade through the increasing availability of
real-time parking lot occupancy data. In this paper, we pursue a statistical
approach for the prediction of parking lot occupancy, where we make use of time
to event models and semi-Markov process theory. The latter involves the
employment of Laplace transformations as well as their inversion which is an
ambitious numerical task. We apply our methodology to data from the City of
Melbourne in Australia. Our main result is that the semi-Markov model
outperforms a Markov model in terms of both true negative rate and true
positive rate while this is essentially achieved by respecting the current
duration which a parking lot already sojourns in its initial state.
