There are a couple issues that can occur within SQL that may cause some server-side performance, which can create performance issues within GlobalSearch.
SQL Server Eating Up All Server RAM
SQL will user as much RAM as it thinks it needs, regardless of the memory consumption of other applications on the server. This can lead to a SQL Server Instance causing a server to become unstable or have performance spikes. You can mitigate this issue by stipulating an upper threshold of memory usage for the SQL Server.
Limit SQL Server Usage
SQL Databases are Constantly Opening and Closing, filling up Event Viewer with Notifications
Often times GlobalSearch databases are set to utilize "Autoclose" which constantly open and close with each connection. This can cause issues with performance both on the SQL side, and needlessly fill up your Event Viewer with verbose data, and in some cases, cause other system issues.
Disable Auto Close
After an Upgrade, System Performance is Much Slower
Some clients may notice some system slowness issues after an upgrade. It may be due to a SQL Upgrade Script not properly running at time of upgrade. This is typically due to an install with insufficient SQL Permissions. Luckily, running the upgrade scripts is easy and can be done within minutes.
Always back up your SQL Server before running any sort of script against a production database. Additionally, large databases may take some time to upgrade. To prevent deadlocks, it's advisable to run these scripts either after hours or off-peak hours.
Run Upgrade Scripts