With the growing number of cloud users and the popularity of cloud services, there has been considerable interest in studying Intercloud models and architectures. Inspired by the existing IEEE P2302 Intercloud framework and standards, this paper presents an Intercloud architecture for Intercloud communications, focusing on resource discovery. An Intercloud system seeks to facilitate the sharing of resources among different clouds so that cloud resources can be used more efficiently and effectively. In general, resources sharing involves three main steps: discovering resources, selecting resources and allocating resources. This paper seeks to study a DNS-based method for discovering cloud resources. Based on an Intercloud architecture, we also develop analytical models by using queuing theory, and examine the impact of different parameters on the performance of the resource discovery process. The performance of two models, sequential search and broadcast search, are compared and analyzed. The main objectives of the modeling are to evaluate the performance and investigate the constraints of these two models, and determine a better resources discovery method that minimizes the average response time.