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Border Gateway Protocol (BGP) is an inter-domain routing protocol that allows an autonomous system (AS) to apply local policies for selecting the best route and decide whether the route information is propagated to other ASes or not. But since the last few years, the research community has shown an increasing interest in the subject of inter-domain routing in optical networks, so there will be need to modify existing BGP with optical counterparts. However, in past few years it is widely accepted now that a multi-domain routing model mostly centered on the exchange of reachability information. So the protocol like the one we have today or the one provided by Optical Border Gateway Protocol (OBGP) is not going to be enough in the future. So routing domains must be able to exchange both, reachability, as well as aggregated Path State Information (PSI). Understanding that there is a missing piece in the routing models provided by BGP and OBGP, but contributing with solutions capable of highly improving the performance of these routing protocols without increasing the number and frequency of the routing messages exchanged between domains is a challenging task. So introduction to the Extended Optical Border Gateway Protocol(OBGP+) was proposed to overcome shortcomings. But when it comes to the case of failure scenario, it is known to us that during convergence BGP withdraws the failed path and selects immediately an alternate path for backup routing. The time required for this convergence should be minimum as possible otherwise the data loss will be enormous. In this paper, Convergence time had been studied for Optical Border Gateway Protocol (OBGP) and Extended Optical Border Gateway Protocol (OBGP+). Extensive simulation of the experiments reveals that OBGP+ is performing better than OBGP in the failure scenarios.