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The Border Gateway Protocol (BGP) is an Inter-Autonomous System (AS) routing protocol currently used in the Internet. The Minimal Route Advertisement Interval (MRAI) plays a prominent role in convergence of the BGP. The previous studies have suggested using the adaptive MRAI and reusable timers to reduce the BGP convergence time. The adaptive MRAI timers perform well under the normal load of BGP update messages. However, a large number of BGP update messages may flood the Internet routers. In this thesis, we propose a new algorithm called MRAI with Flexible Load Dispersing (FLD-MRAI) that reduces the router's overhead by dispersing the load in case of a large number of BGP update messages. We examine the MRAI timers under both the normal and heavy loads of BGP update messages. The proposed algorithm is evaluated using the ns-BGP network simulator and topologies are derived from the BCNET BGP traffic and from various topology generators.