Dynamic scheduling techniques, and EDF (Earliest Deadline First) in particular, have demonstrated their ability to increase the schedulability of real time systems compared to fixed-priority scheduling. In distributed systems, the scheduling policies of the processing nodes tend to be the same as in stand-alone systems and, although few EDF networks exist, it is foreseen that dynamic scheduling will gradually develop into real-time networks. There are some response time analysis techniques for EDF scheduled distributed systems, mostly derived from the holistic analysis developed by Spuri. The convergence of the holistic analysis in context of EDF distributed systems with shared resources had not been studied until now. There is a circular dependency between tasks’ release jitter values, response times and preemption level ceilings of shared resources. In this paper we present an extension of Spuri’s algorithm and we demonstrate that its iterative formulas are non-decreasing, even in the presence of shared resources. This result enables us to assert that the new algorithm converges towards a solution for the response times of the tasks and messages in a distributed system.