##### 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 P_{i} is S_{i} where S_{i}>0.

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

a)∑_{i=1 to n} (S_{i}<m+n)

b) ∑_{i=1 to n} (Si<m*n)

Consider the below scenario.

Assume that all the processes (P

_{i}) are holding S_{i}- 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 ⇒ \(\sum \limits_{i=1}^{n} (S_i ) < (m + n)\)

This question has been discussed before : http://www.techtud.com/doubt/suppose-n-processes-p1-%E2%80%A6-pn-share-m-identical-resource