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Proposed is a novel method to compute the intra-area convergence time of open shortest path first (OSPF) based networks in the presence of designated routers (DRs) on Ethernet and non-broadcast multi-access segments. The capacity of the proposed method is demonstrated by evaluating the convergence time performance of OSFP on internet scale networks (having a thousand autonomous system level routers). The method has also been used to analyse the effects of: (a) the number of DRs, (b) cascading failures, and (c) topological changes on the convergence time of the routers within an area. Furthermore, the time the network takes from a cold state to reach a stable (steady) state in an area is also analysed.