Optical grid networks allow many computing sites to share their resources by connecting them through high-speed links, providing a more efficient use of the resources and a timely response for incoming jobs. These jobs originate from users connected to each of the sites and, in contrast to traditional queueing networks, a particular job does not have to be processed in a predefined site. Furthermore, a job is always processed locally if there is an available local server. In this paper we propose two different methods to approximate the performance of an optical grid network with a ring topology. The first method is based on approximating the inter-overflow time process, while the second separately characterizes the periods where jobs are overflowed and the periods where they are served locally. Both approaches rely on a marked Markovian representation of the overflow process at each station and on reducing this representation by moment-matching methods. The results show that the methods accurately approximate the rate of locally processed jobs, one of the main performance measures.