How to limit the flow of tasks going to a limited pool of resources?

Question

Project management

For example, you have one designer and how to solve the problem of 3 project managers competing for his time.

Answer 1

1. use a project management service and designer load visualization
2. hire another designer, if there is such a high competition, projects will be slowed down. Designers are creative people, they may not meet the deadlines
3. set the priority of projects
4. optimize the work of the designer, freeing him from some tasks

Answer 2

If we take the number of tasks and the number of designers as a constant. There is only one solution - to increase the quality and efficiency of the designer's work.
You can save the designer's time on the contact of managers with him, and not vice versa.
Redirect task flows (with the specified priority) from the designer to the backlog.
The designer himself will pick up tasks from the backlog.
Forbid managers to approach the designer, if he needs something from them, he will call managers himself.

Answer 3

If it is not possible to hire another person (at least for part time), then, I think, the prioritization of existing tasks will help.