@DhavalPadshala

Then we have to look at the configuration files.

Your PHP configuration is located in /etc/php/5.6/fpm/pool.d/ - the listen parameter should be /var/run/php5-fpm.sock.

Are you running Ubuntu 16.04 or 14.04?

@DhavalPadshala

Okay, that's a different problem then.

What's your definition of "high traffic"? And what are you running on the website?

Can you post your PHP pool configuration?

@DhavalPadshala

You either need to make a queue system or increase the processes in the pool.

Since I don't know how much RAM you have available or how consuming the script is, it's hard to know exactly what to put in, but you can play around with it.
Remember to sudo service php5-fpm restart after changes.

I've removed all comments besides two lines to make it easier to manage.

[www]

user = www-data
group = www-data
listen = /var/run/php5-fpm.sock
listen.owner = www-data
listen.group = www-data
listen.mode = 0660

pm = dynamic
; pm.max_children = (total RAM - RAM used by other process) / (average amount of RAM used by a PHP process)
pm.max_children = 15
; pm.start_servers = min_spare_servers + (max_spare_servers - min_spare_servers) / 2
pm.start_servers = 5
pm.min_spare_servers = 5
pm.max_spare_servers = 10

chdir = /

Another solution would be to generate multiple pools and have Nginx load balance between the pools. There's upside/downside to both, so it really depends on your script and what the server is doing.

Have you tested if your script would benefit from using PHP 7 instead of 5 ?
Again, since I don't know what your script is doing, I cannot say if it'll benefit, but almost every script or app I've been using will use much less RAM and runs much-much faster with PHP 7.1, so I would highly recommend that you test that.

@DhavalPadshala No problem, most of us here are non-English speakers :-)

With that amount of RAM and CPU, you can probably set the amount of processes to a fairly high level, but do some testing and slowly increase the numbers.

And you should really look into upgrading your script, so it works with PHP 7, since 5.6 will only be support until the end of 2018:
http://php.net/supported-versions.php