Consider the following snapshot of a system running n concurrent processes.…
2021
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 = Y q = 0. Which one of the following conditions guarantees that no other process apart from p and q can complete execution?
- E.
Question not attempted
Attempted by 92 students.
Show answer & explanation
1. Analyze the state of processes p and q: Since Y_p = 0 and Y_q = 0, these two processes require no additional resources to complete. They will finish execution immediately.
2. Determine available resources: Upon completion, p and q will release their held resources. The total number of resources released is X_p + X_q.
3. Condition for other processes: For no other process (k ≠ p, q) to complete, the available resources (X_p + X_q) must be insufficient for any of them. This means X_p + X_q must be strictly less than the requirement Y_k for every other process k.
4. Mathematical formulation: The condition X_p + X_q < Y_k for all k ≠ p, q is equivalent to X_p + X_q < Min{Y_k | 1 ≤ k ≤ n, k ≠ p, k ≠ q}.