The Border Gateway Protocol (BGP) is the default routing protocol for the routing between autonomous systems in the Internet. BGP’s convergence time is mainly dependent on the Minimum Route Advertisement Interval (MRAI) value, But the influence of this MRAI value on the router’s resources is not yet understood well enough to improve the existing protocol implementation in terms of the specific aspects like CPU utilization, Memory requirement, Bandwidth utilization and convergence time. Therefore it has been analyzed to understand the relationship between the setting of Minimum route advertisement (MRAI) value and the resource requirement of BGP. This paper analyse the convergence times and number of exchanged updates to the different MRAI settings of BGP. In particular, the influence of the MRAI timer in the router CPU utilization, Bandwidth and Memory requirement, number of updates and convergence time is investigated. Designed an algorithm to enhance the convergence time of BGP by considering the minimum route advertisement interval time and reduce routing update overhead. And it shows enhancement of 17% of CPU utilization, 10% of Bandwidth, 10% of memory requirement and 14% of convergence time when compared with the existing system.