Abstract- This paper propose a numerical solution to analyze the impact of implementing different priority in the queuing stations in a shared networks to the performance of the networks. We considers two networks model, chain and bottleneck. In bottleneck network we use two different scenarios, priority and non-priority scenario. In each network, we model the number of job queued in each queuing station using a finite CTMC. This proposed model allows us to investigate performance evaluation properties such as blocking probability, system utilization, delay and system throughput in a bottleneck system and how implementing different priority in the bottleneck node affect them.