Monitoring processor in a circuit switched network is considered. Monitoring processor monitors communication links offers a grade of service in each link to controller. Such an information is useful for an effective maintenance of system. Two links with asymmetric system parameters and multi-symmetric links are respectively considered. Each links is to be an independent M /M/ 1/ 1/ type. Markov modeling technique is used to represent a model of monitoring processor with FCFS steering protocol. Performance measures considered are ratio of monitored jobs in each link, availability of minitoring processor and throughput of virtual processor in each link. The value of the performance meausres are compared with existing and simulation results.