Operating Systems | Deadlock | Question 2

Consider the following snapshot of a system running n processes. Process i is holding Xi instances of a resource R, 1 <= i <= n. currently, all instances of R are occupied. Further, for all i, process i has placed a request for an additional Yi instances while holding the Xi instances it already has. There are exactly two processes p and q such that Yp = Yq = 0. Which one of the following can serve as a necessary condition to guarantee that the system is not approaching a deadlock?
(A) min (Xp, Xq) < max (Yk) where k != p and k != q
(B) Xp + Xq >= min (Yk) where k != p and k != q
(C) max (Xp, Xq) > 1
(D) min (Xp, Xq) > 1


Answer: (B)

Explanation: Since both p and q don’t need additional resources, they both can finish and release Xp + Xq resources without asking for any additional resource. If the resources released by p and q are sufficient for another process waiting for Yk resources, then system is not approaching deadlock.

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