GATE CSE 2019 | Question: 39

Question

Consider the following snapshot of a system running $n$ concurrent processes. Process $i$ is holding $X_i$ instances of a resource $R$, $1 \leq i \leq n$. 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. $X_p + X_q < \text{Min} \{Y_k \mid 1 \leq k \leq n, k \neq p, k \neq q \}$
• B. $X_p + X_q < \text{Max} \{Y_k \mid 1 \leq k \leq n, k \neq p, k \neq q \}$
• C. $\text{Min}(X_p,X_q) \geq \text{Min} \{Y_k \mid 1 \leq k \leq n, k \neq p, k \neq q\}$
• D. $\text{Min}(X_p,X_q) \leq \text{Max} \{Y_k \mid 1 \leq k \leq n, k \neq p, k \neq q\}$

Comments

A is correct

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https://gateoverflow.in/1844/gate2006-66

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It's mentioned in the question,' process i can place a request for atmost Yi additional instances' . Isn't it possible to infer that process i need not require additional resource in some cases or requires less than Yi  ?

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@Arjun sir, please add "Resource-allocation" tag on this question instead of  "process-synchronization" tag.

Answer 1

We have to ensure deadlock.

So, the soon-to-be-available resources ($X_p + X_q$) should not satisfy even the minimum demand of any other process.

Option A

Answer 2

P & Q does'nt require any additional resource & therefore they will complete their execution. After that, they will release there aquired resources.(Xp & Xq). Now these resources will be allotted to the process which need less than or equal to the sum of these resources. If only these two processed will complete it's execution & no other process will, then Xp+Xq < min(request  for resource by all the processes), this condition must be satisfied. Option A is correct.

Answer 3

P & Q does'nt require any additional resource & therefore they will complete their execution. After that, they will release there aquired resources.(Xp & Xq). Now these resources will be allotted to the process which need less than or equal to the sum of these resources. If only these two processed will complete it's execution & no other process will, then Xp+Xq < min(request  for resource by all the processes), this condition must be satisfied. Option A is correct. rest other options may not satisy the condition.