What does it mean that parallel versus sequential agent execution?

Some agents can run simultaneously while others must wait for previous results.

Example: You are planning a cross-country move. Some tasks are independent: researching neighborhoods, getting insurance quotes, and selling furniture can all happen at the same time, handled by different people or by you in any order. But other tasks have hard dependencies: you cannot schedule the movers until you have signed a lease, and you cannot sign a lease until you have chosen a city. If you try to do everything sequentially — finish one task completely before starting the next — the move takes months longer than it needs to. If you try to do everything in parallel — including the tasks with dependencies — you waste effort on quotes for cities you will not choose and schedules for apartments you have not secured. The skill is not choosing parallel or sequential. It is mapping which tasks depend on which, running the independent ones simultaneously, and sequencing only the ones that genuinely require prior results.

Try this: Pick a complex project you are currently working on or planning — a product launch, a career transition, a home renovation, a research paper. List every task involved. For each task, answer one question: 'Does this task require the output of another task before it can begin?' Draw arrows from each dependency to the task it blocks. You now have a dependency graph. Identify every task that has no incoming arrows — these can start immediately and run in parallel. Identify every chain of arrows — these are your sequential constraints. Look at the longest chain. That is your critical path: the minimum time the project will take regardless of how many resources you add. Now ask: am I currently running independent tasks in parallel, or am I needlessly serializing them?