GATE Overflow Test Series | Operating Systems | Test 1 | Question: 26

Question

Consider a system having $k$ resources of the same type. These resources are shared by $5$ processes $A,B,C,D$, and $E$ which have peak demands of $5,7,9,3$ and $8$ respectively. Further it is restricted that at any point of time processes $A$ and $B$ together cannot hold more than $8$ resources whereas no such restrictions are there for processes $C,D$ and $E.$ For which of the following values of $k,$ deadlock may occur? (Mark all the appropriate choices)

• A. $24$
• B. $25$
• C. $27$
• D. $26$

Answer 1

In the worst case for process completion, it should be that each process must hold one less resource than its peak demand. That is processes $A,B,C,D$ and $E$ must be holding $4,6,8,2$ and $7$ number of resources and if no more free resource is there, we have a deadlock. i.e., if the total number of resources is less than or equal to $4+6+8+2+7 = 27$ we can have a deadlock. But there is a further restriction that processes $A$ and $B$ together can hold maximum $8$ resources at a time. This means instead of $4+6$ we added we must do just $8.$ This means, only if the total number of resources is less than or equal to $27 - 10+8 = 25,$ there can be a deadlock.

Comments

If A and B together cannot hold more than 8 resources then how can they ever reach to completion if both are running simultaneously and adequate amount of resources (>= 10) available?

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With any number of resources >8 we can have a deadlock. As here it is given that A and B cannot hold more than 4 resources at a time. Notice that what is required is not the number of resources that would guarantee us a deadlock, but the number of resources with which we MAY have a deadlock. Say we have 100 resources, but have allocated A with 4 and B with 4 resources. Now, A and B together hold 8 resources. There is no way that A can get the extra 1 resource and complete as then A and B would have total more than 8 resources. Same way, B cannot get that extra 3 resource and complete as A and B need to hold a max of 8 resources. In other words, if we ignore everything else and focus on A and B, A and B are in a deadlock within themselves irrespective of the resource count. Please correct me if I am wrong here…

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@Bikram sir we are having problem here can you please explain the answer