GATE CS 2016 Set 2 — Question 59
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Operating System → Process Synchronization → Semaphores
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Question
Consider a non-negative counting semaphore . The operation
P(S) decrements , and V(S) increments . During an execution, P(S) operations and V(S) operations are issued in some order. The largest initial value of for which at least one P(S) operation will remain blocked is _______.Correct answer
7 to 7
Solution
Let the initial value of the semaphore be .
Number of
Number of
The total number of resources available to satisfy these requests is the initial resources plus the resources released by operations:
Total Available = For at least one
Since we are looking for the largest initial value of that satisfies this condition, and must be an integer:
Thus, if , total available is . Since 20 resources are needed, 1 process will remain blocked.
Number of
P(S) operations (decrement) = 20.Number of
V(S) operations (increment) = 12.The total number of resources required by the operations is 20.The total number of resources available to satisfy these requests is the initial resources plus the resources released by operations:
Total Available = For at least one
P(S) operation to remain blocked, the total available resources must be strictly less than the total required resources:Since we are looking for the largest initial value of that satisfies this condition, and must be an integer:
Thus, if , total available is . Since 20 resources are needed, 1 process will remain blocked.
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