The present paper studies a model of a multi-server system operating at multiple processing speeds with random transitions between speeds as customers arrive and depart. This model is also known as the Cluster Model or the Multi-server Job Model. The possibility of reducing the phase space size of the model is substantiated. An algorithm is proposed for constructing an infinitesimal generator matrix to describe the behavior of this model with a reduced phase space. An R-language package implementing this approach, along with an example of its usage, is presented.