How to que large traffic users

we have laravel mobile app with apis and when ever we do campaigns the traffic increases were we send out 100k sms with an offer and the app dies due to server overload, due to limited budget we cannot move to crazy scaling solutions with AWS or GCP and we are happy where we are hosting with a dedicated server with load balancers and one dedicated postgres db

we looking for a solution where my laravel application has huge traffic incoming from 10000 of customers opening the app at the same time which has brought the server down how do i tell my laravel application to serve only 100 to 200 request a minute and show other who are also trying to open the application "app is busy please wait in que" this way the app will not die and people can get served one by one , just like when you want to buy your favourite cake during xmas the famous restaurant owner doesnt allow everyone to flock into his restaurant or bakery but asks the customers to stand in que for hours and hours for their turn