Gómez Corral, AntonioLópez García, MPalacios Rodríguez, FátimaTaipe Hidalgo, Diana Paulina2026-06-052026-06-05202610.1007/s11009-026-10268-9https://hdl.handle.net/20.500.14352/137210For a level-dependent quasi-birth-death process X with time-varying transition rates, we propose a computational approach to compute the probability law of first-passage times to higher levels, as well as related hitting probabilities, at a fixed horizon T < ∞. The approach involves approximating the first-passage time distributions of X at time T by their counterparts in a suitably defined process with piecewise-constant transition rates at an independent, Erlang-distributed horizon with S stages and mean T. The solution is exemplified by numerical experiments in the context of epidemics and queueing models.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal articlehttps://doi.org/10.1007/s11009-026-10268-9https://rdcu.be/fj30jopen accessHitting timesHitting probabilitiesQuasi-birth-death processTime-varyingMatemáticas (Matemáticas)Análisis numéricoProcesos estocásticos12 Matemáticas1206 Análisis Numérico1208.08 Procesos Estocásticos