Consider a system with 3 processes sharing 4 instances of the same resource type. Each process can r

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GATE-CS is a competitive examination conducted in India. This question is from the 2018 GATE-CS Operating Systems paper.

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Question

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

Accepted Answer

Correct Answer: 2Step-by-step Solution:For deadlock to be impossible in all scenarios, the system must always be in a safe state. The necessary and sufficient condition for guaranteeing deadlock avoidance with n processes, R total resources, and each process requesting at most K instances is: n(K − 1) + 1 ≤ R.This condition ensures that even in the worst case — when every process holds K − 1 resources and still needs 1 more — there is at least one resource available to allow some process to complete, release its resources, and enable the others to proceed.Applying: n = 3, R = 4. The condition becomes 3(K − 1) + 1 ≤ 4, so 3K − 3 + 1 ≤ 4, giving 3K ≤ 6, or K ≤ 2. The largest K that always avoids deadlock is 2.Verification for K = 2: worst case has each of 3 processes holding 1 resource (3 allocated), 1 resource remaining in the pool. Each process needs 1 more. At least one process can be granted its request immediately, complete, and release resources, unblocking the others. Safe.Verification for K = 3: each process could hold 2 resources (6 needed, but only 4 available). In a feasible scenario where each holds 1 and needs 2 more, the 1 remaining resource is insufficient for any process to complete. Deadlock is possible.Key Concept: The deadlock-freedom condition for n processes competing for R identical resources with maximum K per process is n(K−1) + 1 ≤ R, equivalently K ≤ 1 + ⌊(R−1)/n⌋. This ensures at least one process can always make progress regardless of the current allocation state.

Consider a system with 3 processes sharing 4 instances of the same resource type. Each process can request a maximum of K instances. Resources 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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Consider a system with 3 processes sharing 4 instances of the same resource type. Each process can request a maximum of K instances. Resources 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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