GATE CS 1992 Q02-xi — Deadlock

To guarantee that the system is deadlock-free, we analyze the worst-case resource allocation scenario.

Let:

• $R = 6$ (total number of tape devices)
• $n$ = number of processes
• $Max_i = 3$ (maximum demand of each process $i$)

In the worst-case scenario, each of the $n$ processes is allocated one resource less than its maximum requirement, and no resources are left free. Under this condition, every process is blocked, resulting in a deadlock.

The maximum number of resources allocated in this worst-case state is:

To guarantee that a deadlock never occurs, the total number of available resources $R$ must be strictly greater than this worst-case allocation, ensuring at least one process can always get its remaining required resource and run to completion:

Substitute the given values into the inequality:

Since the number of processes $n$ must be an integer, the maximum value of $n$ for which the system is guaranteed to be deadlock-free is $2$.