This paper mentions a centralized approach based on SNMP protocol and distributed approach based on mobile agent in network management s system. And it presents a few Quantitative models for systematically evaluating those two different approaches. To do this, we propose model m that is applicable under a uniform network environment, and compare network execution times of each paradigms based on parameters from s simulation. The model is then refined to take into account non-uniform networks. We show that it can reduce overall network execution times b by determining the best interaction patterns to perfo$pi$n network management operations from this model. We believe that the model proposed h here should help us to decide appropriate paradigms and interaction patterns for developing network management applications.