Consider the following snapshot of a system running n concurrent processes. Process i is holding Xi instances of a resource R, 1 ≤ i ≤ n. Assume that all instances of R are currently in use. Further, for all i, process i can place a request for at most Yi additional instances of R while holding the Xi instances it already has. Of the n processes, there are exactly two processes p and q such that Yp = Yq = 0. Which one of the following conditions guarantees that no other process apart from p and q can complete execution?

Consider the following snapshot of a system running n concurrent processes. Process i is holding Xi instances of a resource R, 1 ≤ i ≤ n. Assume that all instances of R are currently in use. Further, for all i, process i can place a request for at most Yi additional instances of R while holding the Xi instances it already has. Of the n processes, there are exactly two processes p and q such that Yp = Yq = 0. Which one of the following conditions guarantees that no other process apart from p and q can complete execution? Correct Answer X<sub>p</sub> + X<sub>q</sub> &lt; Min {Y<sub>k</sub> | 1 ≤ k ≤ n , k ≠ p, k ≠ q}

Process

1

2

3

4

p

q

..

n

Resource instance

Allocated

X1

X2

X3

X4

..

Xp

Xq

Xn

Additional resource

need

Y1

Y2

Y3

Y4

Yp = 0

Yq = 0

Yn

 

All instances of ‘R’ are currently in use. Therefore, available resource = 0

Additional need of process p and q are 0. Therefore, process p and q will release the instances Xp and Xq held by it after its execution.

Available resource = Xp + Xq

To guarantees that no other process apart from p and q can complete execution

Available Resource < minimum of additional resource needed

Xp + Xq < Min {Yk | 1 ≤ k ≤ n, k ≠ p, k ≠ q}

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