GATE CS 2017 Set 2 Q33 — Deadlock

To determine the state of the system, we first calculate the total allocated resources, the available resources, and the remaining need for each process.

1. Calculate Available Resources:

• Total tape drives = $9$
• Total allocated = $\text{Allocation}(P1) + \text{Allocation}(P2) + \text{Allocation}(P3) = 3 + 1 + 3 = 7$
• $\text{Available} = 9 - 7 = 2$

2. Calculate Remaining Need:

• $\text{Need}(P1) = \text{Max}(P1) - \text{Allocation}(P1) = 7 - 3 = 4$
• $\text{Need}(P2) = \text{Max}(P2) - \text{Allocation}(P2) = 6 - 1 = 5$
• $\text{Need}(P3) = \text{Max}(P3) - \text{Allocation}(P3) = 5 - 3 = 2$

3. Find a Safe Sequence:

• With $\text{Available} = 2$, we can satisfy the need of $P3$ since $\text{Need}(P3) = 2 \le 2$. After $P3$ completes and releases its resources, the new available resources become: $$\text{Available} = 2 + 3 = 5$$
• With $\text{Available} = 5$, we can satisfy the need of $P1$ since $\text{Need}(P1) = 4 \le 5$. After $P1$ completes and releases its resources, the new available resources become: $$\text{Available} = 5 + 3 = 8$$
• With $\text{Available} = 8$, we can satisfy the need of $P2$ since $\text{Need}(P2) = 5 \le 8$.

Since a safe sequence $\langle P3, P1, P2 \rangle$ exists, the system is in a Safe state, which guarantees that it is Not Deadlocked.