'Hogging' is a dramatic overstatement. I have a billability target for my job (essentially nearly all of my time needs to be spent working on client work rather than admin/emails). I work in a small team of 6 and we have a shared inbox where tasks come in. When a task comes in, you put your name against it and then move it into a different folder and begin working on it.
Three of my colleagues I regularly find will put their name down on jobs long before they begin to start them. Sometimes it's because it makes sense (e.g. is related to a project they've worked on before), but most of the time it just seems they do it so they can line up tasks for themselves and always have something in the pipeline. It seems productive and efficient and like they're being really helpful but I'm finding it frustrating because there have been so many times recently when there have been no new tasks in and I've had time to start on something. I've posted in our Teams chat offering up my time and no one responds. My billability has been lower than it should be the last few weeks because of this and I have my performance review coming up.
Is offering my time to the wider team enough or should I be doing more?