The following figure shows the behaviour of four periodic tasks: $W,x,Y$ and $Z.$ The priorities

of these tasks are determined by the monotonic rate scheme, having as a result that

priority $(W)>$ priority $(x)>$ priority $(Y)>$ priority $(Z).$

The period of each task starts at time S and ends at time $7.$ The four tasks share $2$

resources that are protected by the binary semaphores A and $B.$ In the above diagram,

label $A($and B$)$ implies a wait operation on the semaphore; label $A^{\text{'}}($and $B^{\text{'}})$ implies a signal

operation on the semaphore.

The process requirements are given in the following table:

The diagram shows the evolution of the execution of the four processes using static

priorities. For example, $x$ starts at time $2,$ successfully executes an operation wait on $B$ at

time $3$ and has to wait on $A$ at time $4($Z had already blocked A$).$ At time $13$ it executes again

$($it has blocked $A),$ activates $A$ at time $14$ and $B$ at time $15.$ It is then evicted by $W$ but executes

again at time $16.$

a$)$ Redo the diagram given in the figure above to illustrate the behaviour of these

processes if priority inheritance is used.

b$)$ Redo the diagram above to show the behaviour of these processes if immediate

priority inheritance is used,

For each diagram, explain the behaviour of the processes shown in the diagrams,

specifying, and explaining how priority inheritance and immediate priority$-$quotient

inheritance are performed, so as to clarify how the diagrams are modified by these

considerations.