This work focuses on the stationary behavior of a simple document processing system. We mean by simple document, any document whose processing, at each stage of its progression in its graph of processing, is assured by a single person. Our simple document processing system derives from the general model described by MOUKELI and NEMBE. It is about an adaptation of the said general model to determine in terms of metrics and performance, its behavior in the particular case of simple document processing. By way of illustration, data relating to a station of a central administration of a ministry, observed over six (6) years, were presented. The need to study this specific case comes from the fact that the processing of simple documents is based on a hierarchical organization and the use of priority queues. As in the general model proposed by MOUKELI and NEMBE, our model has a static component and a dynamic component. The static component is a tree that represents the hierarchical organization of the processing stations. The dynamic component consists of a Markov process and a network of priority queues which model all waiting lines at each processing unit. Key performance indicators were defined and studied point by point and on average. As well as issues specific to the hierarchical model associated with priority queues have been analyzed and solutions proposed; it is mainly infinite loops.