Consider a system consisting of $k$ instances of a resource $R$, being shared by 5 processes. Assume that each process requires a maximum of two instances of resource $R$ and a process can request or release only one instance at a time. Further, a process can request the second instance of the resource only after acquiring the first instance. The minimum value of $k$ for the system to be deadlock-free is ________. (answer in integer)

To guarantee that the system is deadlock-free, the total number of resource instances $k$ must be strictly greater than the maximum number of resources that can be allocated without any single process completing its maximum demand.

Given:

• Number of processes $N = 5$

• Maximum demand of each process $M_i = 2$ for all $i \in \{1, 2, \dots, 5\}$

In the worst-case allocation scenario, each process is allocated one less than its maximum demand:

The total number of instances allocated in this worst-case state is:

To ensure at least one process gets its remaining requested instance, completes execution, and releases all its resources, we need at least 1 additional resource instance:

Thus, the minimum value of $k$ for the system to be deadlock-free is 6.