This research work centers on the performance and stability analysis of the TCP queue based network system. The TCP is a vital organ in every wireless network and due to the increasing reliance on the wireless network by most human activities, it has suffered from different forms of disturbances most especially traffic congestion which eventually results to data loss or total collapse of the network. Many works were reviewed on the TCP model and the methods proposed to improve the performance of the TCP networks. However, from the review, the TCP queue model was not examined based on its performance and reliability, to ascertain the real behavior of the system without the control measures. The step function time domain plot and bode frequency domain plot analyses measures were employed in this work.  From the simulation results, the TCP queue with time delay model recorded a 0% overshoot and settling time of 1.96e+03 seconds. With the high settling time the system performance will be very poor as a result of very slow response and it cannot support the recent high data traffic. Therefore, the system will not be able to solve the problem of congestion due to its slow response. The system also recorded a negative gain margin of -71.9dB, hence; the system is unstable and not reliable.