InfiniBand is becoming increasingly popular in the area of cluster computing due to its open standard and high performance. Fat Tree is a primary interconnection topology for building large scale InfiniBand clusters. Instead of using a shared bus approach, InfiniBand employs an arbitrary switched point-to-point topology. In order to manage the subnet, InfiniBand specifies a basic management infrastructure responsible for discovery, configuration and maintaining the active state of the network. In the literature, simulation studies have been done on irregular topologies to characterize the subnet management mechanism. However, there is no study to model subnet management mechanism on regular topologies using actual implementations. In this paper, we take up the challenge of modeling subnet management mechanism for Fat Tree InfiniBand networks using a popular subnet manager OpenSM. We present the timings for various subnet management phases namely topology discovery, path computation and path distribution for large scale fat tree InfiniBand subnets and present basic performance evaluation on small scale InfiniBand cluster. We verify our model with the basic set of results obtained, and present the results for the model by varying different parameters on Fat Trees.