Skip the Spreadsheet: What-If Analysis with Petri Nets

Every business plan has a spreadsheet. Revenue projections, cost estimates, break-even calculations. They look precise. They're mostly fiction.

The problem isn't the math — it's that spreadsheets can't model flow. Customers arrive, wait, get served, and leave. Staff clock in and out. Rooms fill up and empty. A spreadsheet gives you totals. A simulation gives you bottlenecks.

The Experiment

We gave an LLM a simple prompt: "Model a veterinary clinic's daily operations." No formulas, no programming — just a plain English description of how the clinic works. Patients arrive, get triaged, see a vet or a technician, maybe need surgery or X-rays, then go home.

The LLM produced a Petri net — a kind of flowchart where tokens represent real things (patients, staff, rooms) and the rules enforce real constraints (you can't start surgery without a surgeon and a free operating room and a patient).

Then we hit simulate.

What Came Out

The simulation runs an entire 10-hour clinic day in under a second. Here's what you can see:

Staffing questions answered immediately:

Two veterinarians handle 8 patients/hour comfortably. At 12/hour, queues start building. At 15, the wait time explodes.
Adding a third vet helps — but only if you also have enough exam rooms. Otherwise you've paid for a vet who's waiting for a room.
The receptionist is never the bottleneck. Good to know before you hire a second one.

Room utilization you can watch:

Four exam rooms are enough for normal days. On surgery days, recovery rooms become the constraint — post-op patients occupy them for hours.
The X-ray room sits idle 70% of the time. Probably don't need a dedicated one.

Financial impact in real time:

Each scenario shows revenue, cost of supplies, staff cost, and gross profit updating as the simulation runs.
A "surgery day" with 3 scheduled procedures looks great on paper — until you see it backs up the exam queue and you lose 4 walk-in appointments worth more combined.

Try it yourself: pilot.pflow.xyz/vet-clinic

A Simpler Example: The Coffee Shop

Not every model needs 32 moving parts. A coffee shop model fits on a napkin:

Inputs: beans, water, milk, cups
Outputs: espresso, americano, latte, cappuccino, mocha
Rules: each drink has a recipe (espresso = 18g beans + 30ml water + 1 cup)

The simulation tells you: at normal pace, you run out of cups first. Run a latte promotion? Now milk is the bottleneck. Double your morning rush rate? Cups run out in half the time.

This is the kind of question that takes an hour in a spreadsheet and 10 seconds in a simulation.

Try it: pilot.pflow.xyz/coffeeshop

Why This Works With LLMs

Petri nets have a useful property: they're simultaneously intuitive enough for an LLM to generate and formal enough to simulate precisely. When you describe "patients arrive, wait for a room, see a vet," that maps directly to places and transitions in the model.

This means you can iterate conversationally:

"What if we added a second surgery room?" "What happens during flu season when arrivals double?" "Show me the day if we cut one technician."

Each change adjusts the model. Each simulation gives you real numbers — not guesses, but the logical consequence of the rules you described.

Spreadsheets vs. Simulations

	Spreadsheet	Simulation
Models	Totals and averages	Flow and constraints
Shows	End-of-day numbers	How the day unfolds
Reveals	Cost structure	Bottlenecks
Answers	"How much?"	"What if?"
Updates	Manually	Change one parameter, re-run

A spreadsheet tells you what you'll make if you see 40 patients. A simulation tells you that you can't see 40 patients with 2 vets and 4 exam rooms — you'll max out at 33, and here's exactly why.

Try It

Both demos are live and interactive:

Vet Clinic: pilot.pflow.xyz/vet-clinic — adjust arrival rates, staffing, service mix, and watch the P&L respond
Coffee Shop: pilot.pflow.xyz/coffeeshop — see which ingredient runs out first under different scenarios

The models are built with pflow, an open-source Petri net toolkit. The source is on GitHub.

If you've got a business operation you want to model, describe it to your favorite LLM and ask for a Petri net. You might be surprised how fast "what if" becomes "here's what happens."

For more on the coffee shop model: Coffee Shop Model

For the theory behind continuous simulation: Declarative Differential Models

For how LLMs and formal models work together: Small Models, Not LLMs

For the code generation platform: Petri-Pilot