Suggest reducing tcp_retries2 (#59222)

Adds documentation suggesting reducing `tcp_retries2` on Linux to detect
network partitions more quickly.

Relates #34405

docs/reference/setup/sysconfig.asciidoc

@@ -14,6 +14,7 @@ The following settings *must* be considered before going to production:
 * <<max-number-of-threads,Ensure sufficient threads>>
 * <<networkaddress-cache-ttl,JVM DNS cache settings>>
 * <<executable-jna-tmpdir,Temporary directory not mounted with `noexec`>>
+* <<system-config-tcpretries,TCP retransmission timeout>>
 
 [[dev-vs-prod]]
 [discrete]
@@ -43,3 +44,5 @@ include::sysconfig/threads.asciidoc[]
 include::sysconfig/dns-cache.asciidoc[]
 
 include::sysconfig/executable-jna-tmpdir.asciidoc[]
+
+include::sysconfig/tcpretries.asciidoc[]

docs/reference/setup/sysconfig/tcpretries.asciidoc

@@ -0,0 +1,49 @@
+[[system-config-tcpretries]]
+=== TCP retransmission timeout
+
+Each pair of nodes in a cluster communicates via a number of TCP connections
+which remain open until one of the nodes shuts down or communication between
+the nodes is disrupted by a failure in the underlying infrastructure.
+
+TCP provides reliable communication over occasionally-unreliable networks by
+hiding temporary network disruptions from the communicating applications. Your
+operating system will retransmit any lost messages a number of times before
+informing the sender of any problem. Most Linux distributions default to
+retransmitting any lost packets 15 times. Retransmissions back off
+exponentially, so these 15 retransmissions take over 900 seconds to complete.
+This means it takes Linux many minutes to detect a network partition or a
+failed node with this method. Windows defaults to just 5 retransmissions which
+corresponds with a timeout of around 6 seconds.
+
+The Linux default allows for communication over networks that may experience
+very long periods of packet loss, but this default is excessive for production
+networks within a single data centre as is the case for most {es} clusters.
+Highly-available clusters must be able to detect node failures quickly so that
+they can react promptly by reallocating lost shards, rerouting searches and
+perhaps electing a new master node. Linux users should therefore reduce the
+maximum number of TCP retransmissions.
+
+You can decrease the maximum number of TCP retransmissions to `5` by running
+the following command as `root`. Five retransmissions corresponds with a
+timeout of around 6 seconds.
+
+[source,sh]
+-------------------------------------
+sysctl -w net.ipv4.tcp_retries2=5
+-------------------------------------
+
+To set this value permanently, update the `net.ipv4.tcp_retries2` setting in
+`/etc/sysctl.conf`.  To verify after rebooting, run `sysctl
+net.ipv4.tcp_retries2`.
+
+{es} also implements its own health checks with timeouts that are much shorter
+than the default retransmission timeout on Linux. However these health checks
+must allow for application-level effects such as garbage collection pauses. We
+do not recommend reducing any timeouts related to these application-level
+health checks.
+
+IMPORTANT: This setting applies to all TCP connections and will affect the
+reliability of communication with systems outside your cluster too. If your
+cluster communicates with external systems over an unreliable network then you
+may need to select a higher value for `net.ipv4.tcp_retries2`. For this reason,
+{es} does not adjust this setting automatically.