Final answer:
A resource allocation graph can show a deadlock when three processes, each needing one resource to complete their tasks, are scheduled in a sequence where there are only two resource instances, leading to a situation where each process holds one and waits for another, creating a cycle in the graph that represents deadlock.
Step-by-step explanation:
The question pertains to a scenario in which a system with three processes (P1, P2, and P3) requires access to a resource for the completion of tasks, with only two instances of the resource available. The resource allocation graph can demonstrate how a deadlock situation can occur when scheduling the processes in the order P1, P2, P3, P1, P2, P3. Deadlocks arise where each process holds one instance of the resource and waits indefinitely for the other to release the second instance, thereby halting all progress.
We can visualize this with a resource allocation graph where each process is represented by a circle and each resource instance by a square. Directed edges from processes to resources represent the request of a resource, while edges from resources to processes represent the allocation of a resource. If in the graph, we have a cycle formed, this indicates that the involved processes and resources are in a deadlock condition.
In this case, if P1 and P2 each hold one resource and all three are requesting the additional resource needed for their tasks, a cycle in the graph is created, indicating a deadlock. Here, none of the processes can proceed because each is waiting for a resource held by another process, thus leading to an impasse of resource allocation and task completion.