What is continuous simulation?

Continuous simulation is a method that treats a system's quantities, such as inventory, population, or cash, as amounts that change smoothly instead of in jumps. The computer approximates that smooth change by recalculating the whole system in very small time steps. It matters because many business, health, and policy questions are about rates and accumulations, where the shape of the curve over time is the answer.

How it works

Each quantity is a stock that accumulates its inflows and outflows. At every step the model works out each rate from the current state of the system, then adds the rate multiplied by the time step to the stock. Rates usually depend on other stocks, which creates feedback loops that make growth, decline, or oscillation appear without being programmed in. This is the core of system dynamics, and it relies on stock and flow thinking.

Continuous simulation works with averages and aggregates, so it does not follow individual items. That makes it fast and easy to read, but it hides differences between individuals. Compare it with discrete-event simulation, which follows separate items through queues and events, and with agent-based modeling, which gives each individual its own rules. Choose continuous simulation when you care about large flows and long-run trends, and a discrete or agent approach when individual variation drives the outcome. The accuracy of the result depends on the time step and the integration method.

Example

Say a tank holds 1,000 liters of water. Water flows in at 20 liters per minute, and water leaves at 5 percent of the current level per minute. At the start the outflow is 50 liters per minute, so the level falls. As the level drops, the outflow shrinks, and the level settles where inflow equals outflow, at 400 liters. The curve bends smoothly toward 400 instead of moving in jumps. This is an illustration with round numbers.

How to model it in Machinations

Draw each accumulating quantity as a Pool, inflows as a Source with a resource connection, and outflows as a Drain whose rate depends on the Pool through a state connection. Add a chart of the Pool and Play the diagram to see the curve develop step by step. Use a Lever to change the inflow and watch the final level move.