I track my productivity in a detailed spreadsheet, logging interruptions per hour. In an open office like yours, sales noise could add up to 20% lost time based on studies I've referenced. Requesting set hours in a quiet area is logical if you present data showing output differences.
Frame it with metrics: compare focused vs. distracted periods. I've done this myself and it helped justify changes. Avoid emotional appeals. stick to facts. Managers respond to numbers, not complaints.
Ultimately, if denied, consider noise-cancelling headphones as a backup, but quantify their limitations too.