In this paper an improvement of the schedulability analysis for fixed-priority distributed hard real-time systems is presented. During the analysis it is not sufficient to include the tasks' worst-case execution time, but also the best-case execution time has to be considered, because the lower bound of the execution has a direct impact on the event densities in the system. The presented approach improves the best-case response time analysis introduced by Redell et al. The paper shows how it is possible to calculate a lower bound for the best-case response time using an expressive event model. This new lower bound of the response time will relax the event densities in a distributed system and will therefore lead to more relaxed worst-case response times.