the maximum number of processes which can be running concurrently on a Linux Server is 32768 (value of short int).

Which means at any given time a 32768 processes can exist concurrently on a Linux Server.

However this value can be increased to a larger number by modifying pid_max parameter under
/proc/sys/kernel/ folder.

The setting can be made permanent by adding this parameter to /etc/sysctl.conf.

To increase the number in realtime, execute following command :

echo 33000 > /proc/sys/kernel/pid_max.

Replace 33000 with the maximum number of process you want on your servers.