Journey planning in (schedule-based) public transit networks has attracted interest from researchers in the last decade. In particular, many algorithms aiming at efficiently answering queries of journey planning have been proposed. However, most of the proposed methods give the user a single or a limited number of journeys in practice, which is undesirable in a transportation context. In this paper, we consider the problem of finding $k$ earliest arrival time journeys in public transit networks from a given origin to a given destination, i.e, an earliest arrival journey from the origin to the destination, a second earliest arrival journey, etc. until the $k^{th}$ earliest arrival journey. For this purpose, we propose an algorithm, denoted by Yen-Public Transit (Y-PT), that extends to public transit networks the algorithm proposed by Yen to find the top-$k$ shortest simple paths in a graph. Moreover, we propose a more refined algorithm, called Postponed Yen-Public Transit (PY-PT), enabling a considerable speed up in practice. Our experiments on several public transit networks show that, in practice, PY-PT is faster than Y-PT by an order of magnitude.