This problem demonstrates that although Equation (10.2) for rate monotonic scheduling is a sufficient condition for successful scheduling, it is not a necessary condition (i.e., sometimes successful scheduling is possible even if Equation (10.2) is not satisfied).
a. Consider a task set with the following independent periodic tasks:
• Task P1:C1 = 20; T1 = 100
• Task P2:C2 = 30; T2 = 145
Can these tasks be successfully scheduled using rate monotonic scheduling?
b. Now add the following task to the set:
• Task P3:C3 = 68; T3 = 150
Is Equation (10.2) satisfied?
c. Suppose that the first instance of the preceding three tasks arrives at time.
Assume that the first deadline for each task is the following:
D1 = 100; D2 = 145; D3 = 150
Using rate monotonic scheduling, will all three deadlines be met? What about deadlines for future repetitions of each task?