Railway services are operated following a predefined timetable. However, their execution is often perturbed by unexpected events that make this timetable infeasible. Delay caused by these events is named primary delay, and it implies that trains occupy tracks at times that are different from the planned one. Depending on traffic and track layout, these late occupations may bring to conflicts , in which at least one train must slow down or even stop to preserve safe separation. This slowing down generates secondary delay, which may quickly propagate in the network. Dispatchers can take actions to limit delay propagation, as train rerouting and reschedul- ing. They mostly do so manually. Several optimization approaches have been proposed in the literature to tackle this problem and support dispatchers (Cacchiani et al. , 2014). This prob- lem is named real-time Railway Traffic Management Problem (rtRTMP). The great majority of the existing approaches either focus on geographically limited infrastructures represented mi- croscopically (D'Ariano & Pranzo, 2008, Törnquist Krasemann, 2012, Pellegrini et al. , 2015), or merge some microscopic aspect to a macroscopic representation to deal with large infrastructures (Lamorgese & Mannino, 2015). One of the main challenges of the microscopic based approaches is their computational performance on large-scale networks. To deal with this challenge, few papers try to coordinate traffic management decisions made on several microscopic parts of in- frastructures (Corman et al. , 2012), or on a somehow obtained decomposition of the overall problem. For example, (Luan et al. , 2020) presents various approaches to define decompositions a priori and to force the various traffic management decisions to be coherent. A rather different problem conception is proposed by (Van Thielen et al. , 2018): the decomposition of the problem changes with traffic evolution. Specifically, the paper defines an algorithm based on the so-called dynamic impact zone . As soon as a conflict is detected, first rerouting possibilities for the two involved trains are assessed. If no rerouting possibility exists to eliminate conflicts, the further conflicts that will be generated by the possible resolutions of the considered one are identified and included in the dynamic impact zone. The conflict resolution is then decided by assessing its consequence in terms of delay propagation in the dynamic impact zone if first-come-first-served is applied. In this work, we propose a neighborhood-based traffic management algorithm, following to some extent the problem conception of (Van Thielen et al. , 2018). We model the infrastructure microscopically. Our algorithm consists in making asynchronous traffic management decisions. Asynchronous decisions are made also in (Dal Sasso et al. , 2021), where train movements are split in so called temporal ticks to assess the presence of deadlocks in a single track network with passing loops. In our case, these decisions allow trains to reach their destination aiming at the minimization of delay propagation. Specifically, we identify the neighborhood of a reference train whenever a decision is to be made on its route or on the precedence with respect to another train. This neighborhood includes only the trains that may use track sections in common with the reference one, in the vicinity of the latter's current location and in the very near future. Traffic is then managed by applying an optimization approach as the one by (Pellegrini et al. , 2015), only considering trains in the neighborhood and the identified possibly common track sections. By doing so, alternative routes are taken into account, but they are as short as possible. This allows limiting the size of the instance and hence the optimization time. Moreover, whenever possible, it avoids making decisions that may have to be modified in the future, when the neighborhood is recomputed. However, routes must be long enough to guarantee that no deadlocks occur right out of the neighborhood due to the decisions made here. The algorithm starts identifying the concerned trains and their shortest but long enough routes. Then, it follows the principle that has proved to be successful in (Pellegrini et al. , 2015), simultaneously optimizing routes and schedules. We theoretically show that, in networks with some specific characteristics, this algorithm guarantees the achievement of a deadlock-free network-level solution, if it exists.