Recent papers have pointed out that data traffic exhibits self-similarity, but self-similarity is observed only on a finite timescale. In order to account for that, we introduce the concept of pseudo long-range dependencies. In this paper, we describe a Modulated Markov process producing self-similarity on a finite timescale; the process is quite easy to manipulate and depends only on three parameters (two real numbers and one integer). An advantage of using it is that it is possible to re-use the well-known analytical queuing theory techniques developed in the past in order to evaluate network performance. A quantitative method based on the decomposability theory of Courtois is given to evaluate the domain of validity where the process exhibits pseudo long-range dependencies. The validation on a queuing problem is also discussed. Finally, we analyze the inputs of a statistical multiplexer in the context of a project called Scalability Enhancements for Connection-Oriented Networks (SCONE).