Mobile agents have been successfully developed for collecting and processing network management information in the Internet, telecommunications network and other type of networks. Topological information of a network is important to the network administrator and users. Mobile agent based topology discovery algorithms are proposed for both Internet and multicast networks in this paper. Statistical models are built for analyzing the behavior of the mobile agents performing topology discovery task. The dwell time distribution at a host, life span distribution of a mobile agent, interreport time distribution of a mobile agent and reports interarrival time distribution at the management station are analyzed. These analytical results show great significance to describe the behavior of the mobile agents performing the given task. A clear insight is given into the performance of mobile agents based topology discovery algorithms and modelling the mobile agents with given task.