Using a cyclic real‐time scheduler, suggest a suitable frame size that can be used to schedule three periodic tasks T1, T2, and T3 with the following characteristics:

## Find Frame Size using Cyclic Real Time Scheduler Problem in Real Time System

**Answer:**

For the given task set, an appropriate frame size is the one that satisfies all the required constraints. Let F be the appropriate frame size.

**Constraint 1:**

F>= max{execution time of a task}

F>= 30

**Constraint 2:**

The major cycle M for the given task set T is

M= LCM(100, 80, 150) = 1200

M should be an integral multiple of F. This consideration implies that F can take on the values 30, 40, 60, 100, 120, 150, 200, 300, 400, 600, 1200 and still satisfy Constraint 1.

**Constraint 3:**

To satisfy this constraint, we need to check whether a selected frame size F satisfies the inequality:

2F – GCD(F, pi) <= di for each pi.

Let us first try for F = 30.

**T1: 2*30 – GCD(30, 100) <= 100**

⇒ 60 – 10 <= 100

⇒ Satisfied

**T2: 2*30 – GCD(30, 80) <= 80**

⇒ 60 – 10 <= 80

⇒Satisfied

**T3: 2*30 – GCD(30, 150) <= 150**

⇒ 60 – 30 <= 150

⇒ Satisfied

Therefore, F=30 is a suitable frame size. We can carry out our computations for the other possible frame sizes, i.e. F = 40, 60, 100, 120, 150, 200, 300, 400, 600, 1200, to find out other possible solutions. However, it is better to choose the shortest frame size.

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