In a commercial facsimile network system, a simulation analysis has been performed using ARENA due to the unavailability of theoretical models. The effect of a priority is compared with that of the current FCFS rule on the arriving call blocking rate and transmission time delay. The result shows that the priority rule reduces more service time delay as the arrival rate increases. A simulation analysis procedure is proposed to select optimal in/out port ratio at various hourly arrival rates with a given multiple-place transmission requests ratio.