Q11

A number of processes could be in a deadlock state if none of them can execute due to non-availability of sufficient resources. Let $P_i, 0 \leq i \leq 4$ represent five processes and let there be four resources types $r_j, 0 \leq j \leq 3$. Suppose the following data structures have been used. Available: A vector of length $4$ such that if Available $[i]=k$, there are k instances of resource type $r_j$ available in the system. Allocation. A $5 \times 4$ matrix defining the number of each type currently allocated to each process. If Allocation $[i,j]=k$ then process $p_i$ is currently allocated $k$ instances of resource type $r_j$. Max. A $5 \times 4$ matrix indicating the maximum resource need of each process. If $Max[i,j]=k$ then process $p_i$, may need a maximum of $k$ instances of resource type $r_j$ in order to complete the task. Assume that system allocated resources only when it does not lead into an unsafe state such that resource requirements in future never cause a deadlock state. Now consider the following snapshot of the system.

$$\overset{\Large{\text{Allocation}}}{\begin{array}{|l|lll|} \hline & r_{0} & r_{1} & r_{2} & r_{3} \\\hline p_{0} & 0 & 0 & 1 & 2 \\ p_{1} & 1 & 0 & 0 & 0 \\ p_{2} & 1 & 3 & 5 & 4 \\ p_{3} & 0 & 6 & 3 & 2 \\ p_{4} & 0 & 0 & 1 & 4 \\\hline \end{array}}\quad \qquad \overset{\Large{\text{Max}}}{\begin{array}{|llll|} \hline r_{0} & r_{1} & r_{2} & r_{3} \\\hline 0 & 0 & 1 & 2 \\ 1 & 7 & 5 & 0 \\ 2 & 3 & 5 & 6 \\ 0 & 6 & 5 & 2 \\ 0 & 6 & 5 & 6 \\\hline \end{array}} \qquad \quad \overset{\Large{\text{Available}}}{\begin{array}{|llll|} \hline r_{0} & r_{1} & r_{2} & r_{3} \\\hline 1 & 5 & 2 & 0 \\\hline \end{array}}$$

Is the system currently in a safe state? If yes, explain why.