In this paper we propose a new, more realistic queueing modelling of Discrete Event Dynamic Systems. Being based on the analysis of the real-world complex discrete event systems, the model allows hot only the exploitation of their inherent parallelism, but also the implementation and the efficiency analysis of deadlock detection/recovery and shared resource conflict solving algorithms. Unlike in most approaches developed so far, we consider the case in which the completion of a task is achieved by sequentially running its subtasks on a heterogeneous system composed of homogenous clusters. Moreover, our model makes distinction between processing clusters and system resources. Each cluster is composed of an infinite length queue and of many identical processing units, and is individualised by the type of processing units it contains and by its position in the subtask processing sequence. A parallel simulator based on this model was implemented on a Sequent Balance shared-memory parallel computer. As the simulator allows the interfacing of its input with the Petri Net representation of the simulated system, our approach also represents a new step in the direction of a unitary modelling theory of Discrete Event Dynamic Systems.