The Input /output (I /0) subsystem is often the bottleneck in high performance computer system. Generally, system performance evaluation models were enhanced to include the effect of the I/0 system. In this paper, we modeled the terminal servers which are Indispensable devices In distribution of computer resources. We use M /M /1 Queueing model for find out the point of the system performance FIFO buffer sizes In the terminal server arc the Important fanctions of the system design and could be effected to the overall system functions. We have proposed the of optimal buffer sizes in the model of terminal server for increasing the system performance. We analizing the vatting time for terruanl server using Queueing model. and We find out the reference model result from simulation.