Joint Progress Diagram

operating-systems concurrency

Definition

Joint Progress Diagram

A joint progress diagram (process progress diagram) is a graphical tool illustrating deadlock potential when two processes compete for resources. It maps each process’s progress along perpendicular axes to identify unsafe regions where deadlock becomes unavoidable.

Mechanism

Axes

Horizontal axis represents Process $P_1$ progress; vertical axis represents Process $P_2$ progress.

Conflict Regions

Rectangular areas where a resource is required by both processes. Due to mutual exclusion, the joint execution path cannot enter these areas.

Unsafe Region

A region from which every possible path (moving only right and up) must eventually lead to a dead end where both processes are blocked.

Significance

Deadlock Inevitability

The diagram shows a system can be in a state that is not yet deadlocked, but from which deadlock is inevitable regardless of future scheduling. Deadlock avoidance strategies (e.g., Banker’s algorithm) ensure the execution path never enters an unsafe region.