I am having a website on which it is usually an incured additional charge for excessive usage of bandwidth.

You can increase your bandwidth, or there is one more type of bandwidth measurement that is Unmetered Method.
This type providers cap or control the “top line” speed for a server. Top line speed in Unmetered bandwidth is the total Mbit/s allocated to the server and configured on the switch level. For example, if you purchase 10 Mbit/s Unmetered bandwidth, the top line speed would be 10 Mbit/s. 10 Mbit/s would result in the provider controlling the speed transfers take place while providing the ability for the dedicated server owner to not be charged with bandwidth overages. Unmetered bandwidth services usually incur an additional charge.