  In queuing theory, it is usual to have some models with a "reset" of the
queue. In terms of lattice paths, it is like having the possibility of jumping
from any altitude to zero. These objects have the interesting feature that they
do not have the same intuitive probabilistic behaviour as classical Dyck paths
(the typical properties of which are strongly related to Brownian motion
theory), and this article quantifies some relations between these two types of
paths. We give a bijection with some other lattice paths and a link with a
continued fraction expansion. Furthermore, we prove several formulae for
related combinatorial structures conjectured in the On-Line Encyclopedia of
Integer Sequences. Thanks to the kernel method and via analytic combinatorics,
we provide the enumeration and limit laws of these "lattice paths with
catastrophes" for any finite set of jumps. We end with an algorithm to generate
such lattice paths uniformly at random.
