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.