UGC NET CSE | December 2015 | Part 2 | Question: 29

Question

A system has 4 processes and 5 allocatable resources. The current allocation and maximum needs are as follows:

	Allocated	Maximum	Available
Process A	1 0 2 1 1	1 1 2 1 3	0 0 x 1 1
Process B	2 0 1 1 0	2 2 2 1 0
Process C	1 1 0 1 0	2 1 3 1 0
Process D	1 1 1 1 0	1 1 2 2 1

The smallest value of x for which the above system in safe state is

• A. 1
• B. 3
• C. 2
• D. 0

Answer 1

here need matrix for all process is given below ( by (Max - allocated))

for     A    0  1  0  0  2           B    0  2  1  0  0      C    1  0  3  0  0     D     0  0  1  1  1 

available is  0  0  x  1  1  

so only D can execute for any no of x  as A,B or C need at least one instance  of either of first 2 resource

if x=1 then D can be executed  and will release its allocated resource which is 1 1 1 1 0   then available matrix

 will become   1  1  2  2  1 but with this neither of (A,B,C ) process can be executed as their need matrix is not less than or equal to available matrix so it will result in unsafe state.

if x=2  

then D can be executed  and will release its allocated resource which is 1 1 1 1 0   then available matrix

 will become   1  1  3  2  1   now Process C (with need 1 0 3 0  0 ) can be executed and release its allocated resources

(1 1 0 1  0 ) and then 

available matrix   will become  2   2  3  3  1  so B can be executed and then A (assuming some minor mistake in last resource)  hence it is safe state

so ans is C    x=2

Note :- process A can not be executed for any no of x  as its fifth resource need is 2 which can not be fulfilled