The Minimal Route Advertisement Interval (MRAI) plays a prominent role in convergence of the Border Gateway Protocol (BGP). Previous studies have suggested using adaptive MRAI and reusable timers to reduce the BGP convergence time. The adaptive MRAI timers perform well under the normal load of BGP updates. However, a large number of BGP updates may flood Internet routers. We propose a new algorithm, MRAI with Flexible Load Dispersing (FLD-MRAI), which reduces the router's overhead by dispersing the load in case of a large number of BGP updates. We also examine the MRAI timers under the normal load of BGP updates. Since BGP routing policies play a significant role in preserving the Internet routing stability, we evaluate their impact on BGP convergence time and Route Flap Damping (RFD) algorithms. The proposed algorithms are evaluated using the ns-BGP network simulator.