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

Q. Consider the following snapshot of a system running 𝑛 concurrent processes. Process 𝑖 is holding 𝑋_𝑖 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 𝑌_𝑖 additional instances of R while holding the 𝑋_𝑖 instances it already has. Of the 𝑛 processes, there are exactly two processes 𝑝 and 𝑞 such that 𝑌_𝑝 = 𝑌_𝑞 = 0. Which one of the following conditions guarantees that no other process apart from 𝑝 and 𝑞 can complete execution?

(A) 𝑋_𝑝 + 𝑋_𝑞 < Min {𝑌_𝑘 | 1 ≤ 𝑘 ≤ 𝑛 , k ≠ p, k ≠ q}

(B) 𝑋_𝑝 + 𝑋_𝑞 < Max {𝑌_𝑘 | 1 ≤ 𝑘 ≤ 𝑛 , k ≠ p, k ≠ q}

(C) Min (𝑋_𝑝 , 𝑋_𝑞) ≥ Min {𝑌_𝑘 | 1 ≤ 𝑘 ≤ 𝑛 , k ≠p, k ≠ q}

(D) Min (𝑋_𝑝, 𝑋_𝑞) ≤ Max {𝑌_𝑘 | 1 ≤ 𝑘 ≤ 𝑛 , k ≠ p, k ≠ q}

Ans: X_p + X_q < Min {Y_k ⏐ 1 ≤ k ≤ n, k ≠ p, k ≠ q}

Solution:

Xi → Holding resources for process pi,

Yi → Additional resources for process pi.

As process p and q doesn’t require any additional resources, it completes its execution and available resources are (Xp + Xq)

There are (n – 2) process pi (1< i < n, i ≠ p, q) with their requirements as Yi (1 < i < n, i ≠ p, q). In order to not execute process pi, no instance of Yi should be satisfied with (Xp + Xq) resources, i.e., minimum of Yi instances should be greater than (Xp + Xq).