Test by Bikram | Operating Systems | Test 2 | Question: 15

Question

There are $5$ processes which require resource instances of same type in quantities $23, \ 35, \ 12, \ 43, \ 15$ respectively. The minimum number of resource instances required for preventing deadlock is _______

Comments

@bikram sir,

what's wrong in this 22+34+42+6+12=116

assign 1 less to all greater requirements and (15-12) +3 to second last and 12 to last one.

Answer 1

Let here are n processes in the system and each one needs k instances of a resources to complete. Then the minimum number of resources that you should keep in the system to ensure no deadlock in the system is n*k-n+1 , where n*k = sum of all resources.

its like n*k-n resources are required so that each process can have one less than the resource instance they require.. but still deadlock can occur as each process depend upon other process for one resource instance ..if we provide n*k-n+1 resource instances than the deadlock condition will never occur.

so use this formula here , here n =5 , n*k = 23+35+12+43+15 =  128

so n*k-n+1 = 128-5+1= 123 +1= 124 

Comments

TELL FORUMLA

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hi

bikram..

here u does not elaborate . how it is?

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Yes @wanted 

Let here are n processes in the system and each one needs k instances of a resources to complete. Then the minimum number of resources that you should keep in the system to ensure no deadlock in the system is n*k-n+1 , 

because  there can be deadlock if none of the process have the required resources, i.e. if each have (k-1).meaning total n*(k-1).now even if there is 1 more resource, there canot be deadlock.so minimum requirement is n*(k-1)+1 = n*k-n+1 .

its like n*k-n resources are required so that each process can have one less than the resource instance they require.. but still deadlock can occur as each process depend upon other process for one resource instance ..if we provide n*k-n+1 resource instances than the deadlock condition will never occur.

so use this formula here , here n =5 , n*k = 23+35+12+43+15 =  128

so n*k-n+1 = 128-5+1= 123 +1= 124 

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Total resources ≥ n × (max_need - 1) + 1
n= no of processes
Where the "+1" ensures at least one process can complete.

Here, out of 5 processes, 4 can execute with" max_need -1", but at least 1 process should get all the resources: so it can complete the task and release the held resourses
min resources needed: 
(23-1)+(35-1)+(12-1)+(43-1)+15 = 22+34+11+42+15= 124