##### explain reason for other option is incorrect ?

Suppose "n" processes P1____Pn , shares "m" identical units, which can be reserved one at a time. The Maximum Resource Requirement of Process Pi is Si where Si>0.

Which of the following is a sufficient condition for ensuring that deadlock  does not occur?

a)∑i=1 to n  (Si<m+n)

b) ∑i=1 to n  (Si<m*n)

Arul
22 Sep 2015 03:16 am

Consider the below scenario.

Assume that all the processes (Pi) are holding Si - 1 resources. (i.e., each process is short of 1 resource to complete it's execution). In this scenario, if it is possible to have atleast 1 extra resource, then all processes can complete the execution. hence, deadlock won't occur.

To put this thought into an equation, for the deadlock to not to occur,

${(m - \sum \limits_{i=1}^{n} (S_i - 1))} > 0$

i.e., $\sum \limits_{i=1}^{n} (S_i - 1) < m$   gives ⇒ $\sum \limits_{i=1}^{n} (S_i ) < (m + n)$

Vivek Vikram Singh
22 Sep 2015 02:05 pm