RDS server come up with 40 connection max, as in the following documentation
I am using Magento 1.9, and at some points, i reach the max number then website is out of service.
Do you have any recommended way to solve this issue?

From my understanding, if i have 2 web servers connection to an RDS server.. then I should have 2 RDS connections, not more.

Best Answer

Aws rds max_connections limit variable is based on instance type, so you can upgrade your rds or make more replica.

The rds types with max_connections limit.

t2.micro 66
t2.small 150
m3.medium 296
t2.medium 312
m3.large 609
t2.large 648
m4.large 648
m3.xlarge 1237
r3.large 1258
m4.xlarge 1320
m2.xlarge 1412
m3.2xlarge 2492
r3.xlarge 2540

Referring by max_connections at AWS RDS MySQL Instance Sizes in 2015

Update 2017-07

The current RDS MySQL max_connections setting is default by {DBInstanceClassMemory/12582880} , if you use t2.micro with 512MB RAM, the max_connections could be (512*1024*1024)/12582880 ~= 40, and so on.

Each web server could have several connections to rds which depend on your sql requests from the web server