GATE CS 2026 Set 1 — Question 35
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Operating System → Deadlocks → Deadlock Numericals
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Question
Consider a system consisting of instances of a resource , being shared by 5 processes. Assume that each process requires a maximum of two instances of resource and a process can request or release only one instance at a time. Further, a process can request the second instance of the resource only after acquiring the first instance.The minimum value of for the system to be deadlock-free is ________. (answer in integer)
Correct answer
6 to 6
Solution
Let be the number of processes and be the maximum requirement of resources for each process.
Given:
The condition for a system to be deadlock-free is that the total number of resources must be at least one greater than the sum of the maximum resources each process can hold without completing.The worst-case scenario for deadlock is when every process holds resources and needs 1 more to proceed.
Maximum resources held in deadlock state = .If the system has 5 resources, each of the 5 processes can hold 1 resource, and none can proceed (deadlock).
To avoid deadlock, we need at least one more resource so that one process can acquire its required 2 instances, finish, and release resources.Minimum
.
Given:
The condition for a system to be deadlock-free is that the total number of resources must be at least one greater than the sum of the maximum resources each process can hold without completing.The worst-case scenario for deadlock is when every process holds resources and needs 1 more to proceed.
Maximum resources held in deadlock state = .If the system has 5 resources, each of the 5 processes can hold 1 resource, and none can proceed (deadlock).
To avoid deadlock, we need at least one more resource so that one process can acquire its required 2 instances, finish, and release resources.Minimum
.
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