Consider a system with 3 processes that share 4 instances of the same resource type. Each process can request a maximum of $K$ instances. Resource instances can be requested and released only one at a time. The largest value of $K$ that will always avoid deadlock is _______.

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Official answer: 2

Deadlock

For a system with $N$ processes sharing $R$ identical resource instances, where each process requires at most $K$ resources, the condition to guarantee that deadlock will never occur is:

\sum_{i=1}^{N} (\text{Max}_i - 1) < R

Since all $N$ processes have the same maximum requirement $K$ :

N(K - 1) + 1 \le R \implies N(K - 1) < R

Given $N = 3$ and $R = 4$ :

3(K - 1) < 4

3(K - 1) \le 3

K - 1 \le 1

K \le 2

Thus, the largest value of $K$ that will always avoid deadlock is 2.

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This Deadlock previous year question is Q24 of the GATE CSE 2018 paper. Find more GATE CSE PYQs on Deadlock in Operating Systems, or browse all GATE CSE PYQs.

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Deadlock in GATE CSE

Deadlock has 11 GATE CSE PYQs across 10 papers from 2014 to 2026. 2 of them are 1-mark NAT questions like this one, and it is the only one in GATE CSE 2018.

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