I was once put in exactly this position. Our IT Manager was fired and I was put in charge of about a dozen sysadmin and helpdesk people. They had over 130 open tickets and claimed to be too busy to do anything. Bear in mind I knew little about infrastructure (I was an applications dev and tech lead who had become a 3rd line application support leader).

I spent a month doing triage, and sorting out their process (they were doing triage, but gave it to a relatively weak member of staff who couldn't spot patterns or kill off tickets effectively). The number came down to 30, and the team was far more focussed. I also got to see who was helping and who wasn't, and sacked another member of staff who bullied less knowledgeable members of the team (while doing literally nothing but spreading FUD).

The point (obvious to anyone who's read The Goal, which I hadat that point) is that the graph doesn't tell you jack about what's going on. You have to go and look. The incoming tickets pipe was the first place to go because it's the simplest firehose to plug. That gave people space to get off the ticket treadmill and work on longer term tech debt.