In this paper we present a new technique which exploits timing-correlation between tasks for scheduling analysis in multiprocessor and distributed systems with tree-shaped task-dependencies. Previously developed techniques also allow capturing and exploiting timing-correlation in distributed systems. However, they are only suitable for linear systems, where tasks cannot trigger more than one succeeding task. The new technique presented in this paper, allows capturing timing-correlation between tasks in parallel paths in a more accurate way, enabling its exploitation to calculate tighter bounds for the worst-case response time analysis for tasks scheduled under a static priority preemptive scheduler.