Question B $(18$ points$)$ Course name

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$$Real time systems

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$$CPRE $558$

Consider three dependent tasks $T_1,T_2,$ and $T_3.$ In order to describe this task set

with the critical sections, we add new parameters that specify the

computation time, $c_i,$ as follows:

${*}_i^x$ : task's computation before entering the critical section.

$*c_i^y$ : task's computation inside the critical section.

$*c_i^z$ : task's computation after the critical section.

That is$,c_i=c_i^x+c_i^y+c_i^z.$

The task set is described by the parameters given in the following table.

Assume the priorities of highest priority task is $3,$ medium priority task is $2,$

and the lowest priority task is $1.$

Answer the following:

Construct the schedule obtained under the RMS algorithm upto

LCM $($periods$).$ Indicate at what point priority inversion occurs.

Construct the schedule obtained using RMS algorithm with Priority

Ceiling Protocol $($PCP$)$ enabled. In your answer, indicate the priority

ceilings for the semaphores.