If you want to bind Puma to a unix socket, you can do this either by providing a -b options:

$ puma -b unix:///var/run/puma.sock

or using a puma.rb config file and setting the bind options.

# puma.rb config file
# ...config...
bind 'unix://var/run/puma.sock'
# ...config

Unfortunately if you try to bind multiple Pumas to one socket, you might end up with issue similar to this one:

2015/02/16 12:12:22 [error] 2476#0:
 *16083152 upstream timed out (110: Connection timed out) while reading response header from upstream, client: 64.251.13.85, server: app,
  request: "POST /notifier_api/v2/notices HTTP/1.1", upstream: "http://unix:///var/run/puma.sock:/notifier_api/v2/notices", host: "app"
2015/02/16 12:12:23 [error] 2476#0:
 *16083176 upstream timed out (110: Connection timed out) while reading response header from upstream, client: 64.251.10.203, server: app,
  request: "POST /notifier_api/v2/notices HTTP/1.1", upstream: "http://unix:///var/run/puma.sock:/notifier_api/v2/notices", host: "app"
2015/02/16 12:12:23 [error] 2474#0:
 *16083180 upstream timed out (110: Connection timed out) while reading response header from upstream, client: 64.251.13.85, server: app,
  request: "POST /notifier_api/v2/notices HTTP/1.1", upstream: "http://unix:///var/run/puma.sock:/notifier_api/v2/notices", host: "app"
2015/02/16 12:12:43 [error] 2476#0:
 *16083282 upstream timed out (110: Connection timed out) while reading response header from upstream, client: 64.251.13.85, server: app,
  request: "POST /notifier_api/v2/notices HTTP/1.1", upstream: "http://unix:///var/run/puma.sock:/notifier_api/v2/notices", host: "app"
2015/02/16 12:12:43 [error] 2476#0:
 *16083292 upstream timed out (110: Connection timed out) while reading response header from upstream, client: 64.251.13.85, server: app,
  request: "POST /notifier_api/v2/notices HTTP/1.1", upstream: "http://unix:///var/run/puma.sock:/notifier_api/v2/notices", host: "app"
2015/02/16 12:12:43 [error] 2476#0:
 *16083301 upstream timed out (110: Connection timed out) while reading response header from upstream, client: 64.251.13.85, server: app,
  request: "POST /notifier_api/v2/notices HTTP/1.1", upstream: "http://unix:///var/run/puma.sock:/notifier_api/v2/notices", host: "app"
2015/02/16 12:13:33 [error] 2474#0:
 *16083390 upstream timed out (110: Connection timed out) while reading response header from upstream, client: 64.251.13.85, server: app,
  request: "POST /notifier_api/v2/notices HTTP/1.1", upstream: "http://unix:///var/run/puma.sock:/notifier_api/v2/notices", host: "app"
2015/02/16 12:13:33 [error] 2474#0:
 *16083392 upstream timed out (110: Connection timed out) while reading response header from upstream, client: 64.251.13.85, server: app,
  request: "POST /notifier_api/v2/notices HTTP/1.1", upstream: "http://unix:///var/run/puma.sock:/notifier_api/v2/notices", host: "app"
2015/02/16 12:13:33 [error] 2474#0:
 *16083397 upstream timed out (110: Connection timed out) while reading response header from upstream, client: 64.251.13.85, server: app,
  request: "POST /notifier_api/v2/notices HTTP/1.1", upstream: "http://unix:///var/run/puma.sock:/notifier_api/v2/notices", host: "app"
2015/02/16 12:13:33 [error] 2474#0:
 *16083398 upstream timed out (110: Connection timed out) while reading response header from upstream, client: 64.251.13.85, server: app,
  request: "POST /notifier_api/v2/notices HTTP/1.1", upstream: "http://unix:///var/run/puma.sock:/notifier_api/v2/notices", host: "app"
2015/02/16 12:13:43 [error] 2477#0:
 *16083428 upstream timed out (110: Connection timed out) while reading response header from upstream, client: 64.251.13.85, server: app,
  request: "POST /notifier_api/v2/notices HTTP/1.1", upstream: "http://unix:///var/run/puma.sock:/notifier_api/v2/notices", host: "app"

So, what is the reason? Your one and only socket might just not be enough. You can call bind multiple times, to create multiple sockets that your clustered Puma will use:

# ...config...
bind 'unix://var/run/puma1.sock'
bind 'unix://var/run/puma2.sock'
bind 'unix://var/run/puma3.sock'
bind 'unix://var/run/puma4.sock'
bind 'unix://var/run/puma5.sock'
# ...config...

Btw great docs for Puma - it's nowhere mentioned and the easiest place to understand how it works, is in the source code, that looks like that:

 # Bind the server to +url+. tcp:// and unix:// are the only accepted
# protocols.
#
def bind(url)
@options[:binds] << url
end