I am trying to simulate in Simulink a model of a control system with queue MM1K from the book Feedback Control of Computing Systems. The book says that this is just a block diagram, so I understand that it will not exactly match with what I want to model in Simulink. However, I don't think it will be very complicated to do it in Simulink. I am a newbie in Simulink. How should I start to model this feedback loop system in Simulink?
Simulink is designed so that it's easy to simulate control loops. All you need to do is choose the blocks you want from the library browser and connect them with arrows. You can also choose initial conditions and select which matlab ode solver you want. All of that will be covered in any basic tutorial on Simulink.
The picture you've posted is a generic diagram of a SISO servo loop. There's nothing you can simulate until you have an actual expression for the controller and plant transfer functions and reference signal.