Linking two Threads in a Client-Server Socket program - Java

I create threads of class A and each sends a serialized object to a Server using ObjectOutputStream.

The Server creates new Threads B for each socket connection (whenever a new A client connects)

B will call a synchronized method on a Shared Resource Mutex which causes it (B) to wait() until some internal condition in the Mutex is true.

In this case how A can know that B is currently waiting?

Note:
A is a GUI. each serialized object sent over socket is added to a queue in Mutex. So, at a particular time if the queue becomes full, B will have to wait till it frees some slots in the queue. So the end user (A GUI thread) has to see a message like "Please wait while a slot becomes free"

. User will have to wait for a reply from B (when it becomes notified by Mutex) in order to continue operations in the GUI (i.e: click a button to open the next JFrame and carry on work)...

How each class is dependent.

(A1 = an instance of class A)

A1--------->B1-------->| ------ |
A2--------->B2-------->| Mutex |
A3--------->B3-------->| ------ |

Hope this description is clear. Thanks in advance.

Can 'B' set a flag before going to wait and reset it after the wait is over? This way A can know if B is waiting.