If the system contains exactly one non-shareable resource instance in total,…

Concept

A deadlock is a permanent circular wait: each process in a cycle waits for a resource held by the next process in that cycle.

Contention alone is not deadlock. When the system has only one non-shareable resource instance in total, its holder has no different resource in this model to wait for, so a circular wait among competing processes cannot form.

Application

Represent the situation with a wait-for graph.

1. If one process holds the single resource instance, every other competing process can only wait for that holder.

2. The holder has no second resource in this model to wait for, so no edge can lead from the holder back to a waiting process.

3. Therefore, the graph has waiting edges but no directed cycle, regardless of whether one, two, or more than two processes compete.

Contrast

• More than two processes: several processes may queue behind one holder, but the queue does not create a cycle.

• Exactly two processes: one may wait for the holder, but there is no return wait that closes a cycle.

• Exactly one process: there is no inter-process waiting cycle.

• None of these cases: process count alone cannot create circular wait with a single resource instance.

Cross-check

All four Coffman conditions are necessary for deadlock. The circular-wait condition is absent here, so the result is none of these cases.