Optical Border Gateway Protocol (OBGP) is an extension to Border Gateway Protocol (BGP) for the Optical Cross Connects (OXCs) to be automatically setup and multiple direct optical lightpaths between many different autonomous domains. With OBGP, the routing component of a network may be distributed to the edge of the network while the packet classification and forwarding is done in the core. However, it is necessary to analyze the stable convergence functions of OBGP in case of lightpath failures. In this paper, we first describe the architecture of OBGP model and analyze the potential problems of OBGP, e.g. convergence behavior virtual BGP router in the lightpath failure. We then propose an OBGP convergence model derived from inter-AS relationship. The evaluation results show that the proposed model can be used for setting stable OBGP routing policy.