Abstract. We propose a method to study M/E_S/1/m, E_r/E_S/1/m, and E_r/M/n/m queueing systems, including the case of m=∞. Recurrence relations are obtained to compute the stationary distribution of the number of customers in the system and the steady-state characteristics. The developed algorithms are tested on examples using simulation models constructed with the assistance of the GPSS World tools .

Keywords: queueing systems, Erlangian distribution, fictitious phase method, recurrence relations, steady-state characteristics.