System Dynamics Applications / F / F.4

F.4 MODULE—TRANSITIONAL (REVERSIBLE) FLOW

F.4.1 General Description

As depicted at Figure F4-1, transitional (reversible) flow occurs back and forth between two stocks. The Transition Rate rate-controlling variable is connected to the valves in each of the pipes. Each of the flows can vary from zero to a maximum value (practically limited by the capacity of the pipes). Without additional outflows or inflows, which are frequently connected in practice, this is a closed-loop system. Each stock can drain to, or fill from, the other.

F.4.2 Module Influence Diagram

The influence diagram for this module is shown in Figure F4-2.

F.4.3 Reference Source

An application of module is described by Sterman (2000: 342-343).

F.4.4 Application

In continuous models, we would envisage flow of a fixed amount of water from one bathtub to another connected bathtub. One bathtub empties as the other one fills. A physical example of this is the swapping between potential and kinetic energy as a simple (ideal) pendulum swings. This is explained in Chapter 1.

Sterman (2000: 342) describes the Bass diffusion model in which people have adopted a product or are potential adopters of that product, there being only two states ADOPTERS and POTENTIAL ADOPTERS. Those who had adopted the product but discard it re-enter the potential customer pool. Others from the potential customer pool adopt the product.

A variation on this application might depict the deployment of limited resources between two modes. Alternatively, limited resources might be deployed between two sites, as might occur in the management of a project.

In a discrete event model, that is, where rates take on discrete values (either 0 or 1, for example), this module could be used to depict a flip-flop logic device where STOCK 1 would take on the value 0 or 1 when STOCK 2 takes on the corresponding values of 1 or 0. In such a case, Transition Rate 1 to 2 and Transition Rate 2 to 1 would be connected or replaced by a single Transition Rate variable.

F.4.5 Functional Description

The functions of the various parts of the module are described in Table F4-1.

Table F4-1. Functional Description—Transitional (Reversible) Flow