networking - Increasing the maximum number of TCP/IP connections in Linux
I am programming a server and it seems like my number of connections is being limited since my bandwidth isn't being saturated even when I've set the number of connections to "unlimited".

Maximum number of connections are impacted by certain limits on both client & server sides, albeit a little differently.
On the client side:
Increase the ephermal port range, and decrease the tcp_fin_timeout
To find out the default values:
sysctl net.ipv4.ip_local_port_range
sysctl net.ipv4.tcp_fin_timeout

The ephermal port range defines the maximum number of outbound sockets a host can create from a particular I.P. address. The fin_timeout defines the minimum time these sockets will stay in TIME_WAIT state (unusable after being used once).
Usual system defaults are:

net.ipv4.ip_local_port_range = 32768   61000
net.ipv4.tcp_fin_timeout = 60

This basically means your system cannot consistently guarantee more than (61000 - 32768) / 60 = 470 sockets per second. If you are not happy with that, you could begin with increasing the port_range. Setting the range to 15000 61000 is pretty common these days. You could further increase the availability by decreasing the fin_timeout. Suppose you do both, you should see over 1500 outbound connections per second, more readily.
To change the values:
sysctl net.ipv4.ip_local_port_range="15000 61000"
sysctl net.ipv4.tcp_fin_timeout=30

The above should not be interpreted as the factors impacting system capability for making outbound connections per second. But rather these factors affect system's ability to handle concurrent connections in a sustainable manner for large periods of "activity."
Default Sysctl values on a typical Linux box for tcp_tw_recycle & tcp_tw_reuse would be
net.ipv4.tcp_tw_recycle=0
net.ipv4.tcp_tw_reuse=0

These do not allow a connection from a "used" socket (in wait state) and force the sockets to last the complete time_wait cycle. I recommend setting:
sysctl net.ipv4.tcp_tw_recycle=1
sysctl net.ipv4.tcp_tw_reuse=1 

This allows fast cycling of sockets in time_wait state and re-using them. But before you do this change make sure that this does not conflict with the protocols that you would use for the application that needs these sockets. Make sure to read post "Coping with the TCP TIME-WAIT" from Vincent Bernat to understand the implications. The net.ipv4.tcp_tw_recycle option is quite problematic for public-facing servers as it won’t handle connections from two different computers behind the same NAT device, which is a problem hard to detect and waiting to bite you. Note that net.ipv4.tcp_tw_recycle has been removed from Linux 4.12.
On the Server Side:
The net.core.somaxconn value has an important role. It limits the maximum number of requests queued to a listen socket. If you are sure of your server application's capability, bump it up from default 128 to something like 128 to 1024. Now you can take advantage of this increase by modifying the listen backlog variable in your application's listen call, to an equal or higher integer.
sysctl net.core.somaxconn=1024

txqueuelen parameter of your ethernet cards also have a role to play. Default values are 1000, so bump them up to 5000 or even more if your system can handle it.
ifconfig eth0 txqueuelen 5000
echo "/sbin/ifconfig eth0 txqueuelen 5000" >> /etc/rc.local

Similarly bump up the values for net.core.netdev_max_backlog and net.ipv4.tcp_max_syn_backlog. Their default values are 1000 and 1024 respectively.
sysctl net.core.netdev_max_backlog=2000
sysctl net.ipv4.tcp_max_syn_backlog=2048

Now remember to start both your client and server side applications by increasing the FD ulimts, in the shell.
Besides the above one more popular technique used by programmers is to reduce the number of tcp write calls. My own preference is to use a buffer wherein I push the data I wish to send to the client, and then at appropriate points I write out the buffered data into the actual socket. This technique allows me to use large data packets, reduce fragmentation, reduces my CPU utilization both in the user land and at kernel-level.
