Throw at random $n$ points, sequentially, on a unit circle and append clockwise an arc (or rod) of length $s$ to each such point. The obtained random set (the free gas of rods) is a union of a random number of clusters with random sizes modelling a free deposition process on a 1D substrate. A variant of this model is investigated in order to take into account the role of disorder $\theta >0$. It involves Dirichlet$\left( \theta \right) $ distributions. For such free deposition processes at disorder $\theta $, we shall be interested in the occurrence times and probabilities, as $n$ grows, of two specific types of configurations: those avoiding rods' overlap (the hard rods gas) and those for which the largest gap is smaller than rods' length $s$ (the packing gas). Special attention is paid to the thermodynamic limit when $ns=\rho $, for some finite density $\rho $ of points. The occurrence of parking configurations, as those for which hard rods and packing constraints are both fulfilled, is then studied. Finally, some aspects of these problems are investigated in the low disorder limit $\theta \downarrow 0$, $n\uparrow \infty $ while $n\theta =\gamma >0$. Here, Poisson-Dirichlet$\left( \gamma \right) $ partitions play some role.
