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GO Classes DPP | OS | RESOURCE ALLOCATION

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A system has $4$ processes $(P_1$ to $P_4)$ and $10$ instances of a single resource type $R$. Each process requires a maximum of $m$ instances to complete. What is the MAXIMUM value of $m$ such that the system is guaranteed to be deadlock-free, regardless of the order in which processes request and release resources?

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\begin{aligned}
&\text {To ensure a system is guaranteed to be deadlock-free, the total resources } R \text { must satisfy: }\\\\
&R \geq \sum\left(\text { Max_Need }_i-1\right)+1\\\\
& 10 \geq 4(m-1)+1 \\\\
& 10 \geq 4 m-4+1 \\\\
& 10 \geq 4 m-3 \\\\
& 13 \geq 4 m \\\\
& m \leq 3.25
\end{aligned}
$\text { Since } m \text { must be an integer, the maximum value is } 3 \text {. }$
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