Before revision:  the special cases of this model correspond to specific examples of different types of cell appendages . Exploiting the techniques of level crossings developed for random excursions of stochastic process, we have derived analytical expressions of passage times for hitting various thresholds, sojourn times of random excursions beyond the threshold and the extreme lengths attained during the lifetime of these protrusions.
After revision:  the special cases of this model correspond to specific examples of different types of cell appendages . Exploiting the techniques developed for the calculation of level-crossing statistics of random excursions of stochastic process, we have derived analytical expressions of passage times for hitting various thresholds, sojourn times of random excursions beyond the threshold and the extreme lengths attained during the lifetime of these protrusions.